Radioactive bone cement

ABSTRACT

A target tissue can be treated with a radioisotope. Some methods for treating a target tissue with a radioisotope include determining a distance between a target tissue and a surface of a matrix material to be positioned adjacent the target tissue and, based on the determined distance, determining an activity to be mixed with the matrix material to obtain a desired activity concentration. Some methods further include mixing the radioisotope with the matrix material. In some embodiments, the matrix material comprises bone cement, and the target tissue is a tumor in a bone. The radioisotope may be a beta-emitting radioisotope mixed in the cement at a concentration to form a radioactive cement.

RELATED APPLICATION

This application is a divisional of U.S. application Ser. No.14/938,708, filed Nov. 11, 2015, which is a continuation of U.S.application Ser. No. 13/403,915, filed Feb. 23, 2012, now U.S. Pat. No.9,198,989, which claims priority benefit under 35 U.S.C. 119(e) fromU.S. Provisional Application No. 61/445,959, filed Feb. 23, 2011, theentirety of each of the above applications is incorporated by referenceherein.

GOVERNMENT LICENSE RIGHTS

This invention was made with Government support under Grant No.W81XWH-07-1-0397, awarded by the ARMY. The Government has certain rightsin this invention.

BACKGROUND

Spinal metastases are a common manifestation of many types of cancer.Specifically, metastatic lesions in the spine have been found in 90.5%,74.3% and 45% of patients who died from prostate, breast and lungcancer, respectively. Additionally, approximately 200,000 patients diewith metastatic lesions in their spine each year in the United Statesalone. Vertebral metastases cause pain, can degrade bone strength, and,due to the proximity of the spinal cord, can lead to seriousneurological complications resulting from vertebral collapse. Treatmentmust address the tumor itself as well as the structural deficiency itmay cause in the bone. The conventional treatment often occurs in twosteps—a surgical procedure in which polymethylmethacrylate (PMMA) bonecement is injected into the vertebral body to restore strength to thebone (vertebroplasty or kyphoplasty), followed by multiple dailyradiotherapy sessions to control tumor growth. The most common type ofradiotherapy for spinal metastases is external beam radiation therapy(EBRT). Although EBRT effectively delivers radiation to the vertebralbody, adjacent radiosensitive tissues such as the spinal cord and nervesare also irradiated, often limiting the dose that can be safelydelivered to the tumor. Thus, to maximize treatment effectiveness whileminimizing collateral damage to normal tissue, EBRT is fractionated intoten daily treatment sessions, inconveniencing patients whose quality oflife has already been compromised. Intensity modulated radiation therapy(IMRT) and stereotactic body radiation therapy (SBRT) have emerged asimproved radiotherapy techniques, but both techniques still requiremultiple treatment sessions, still irradiate the spinal cord and nerves(albeit to a lesser extent), and are expensive.

The use of vertebroplasty and kyphoplasty is likely to increase, as bothprocedures can provide immediate pain relief and patients withmetastatic bone disease are living longer. However, conventionalradiation therapy modalities can be inconvenient for the patient, asthey are performed separately from the surgical procedure and areusually fractionated into multiple treatment sessions to minimize thecollateral damage to normal tissue that occurs when radiation isdelivered using an external irradiation source. Although radiotherapycan be given in fewer fractions with similar pain relief, patientstreated with a single fraction tend to require retreatment more oftenthan patients treated with multiple fractions.

SUMMARY

Described herein are methods for treating a target tissue with aradioisotope that include determining a distance between a target tissueand a surface of a matrix material to be positioned adjacent the targettissue and, based on the determined distance, determining an activity tobe mixed with the matrix material to obtain a desired activityconcentration. Some methods further include mixing the radioisotope withthe matrix material. In some methods, the surface comprises a closestsurface of the matrix material to the target tissue. In some methods,the closest surface may be a point on the surface or a small regionabout the point that is the minimum distance to the target tissue. Thematrix material may be a bone cement. The target tissue may be a bonetumor. As used herein, a “bone tumor” or “a tumor in a bone” may includea primary tumor, a secondary tumor, or the presence of both in a bone.

Some methods are described herein for determining an activityconcentration of a radioisotope for treating a target tissue in avertebra. Some methods include, based on (a) a distance between thetarget tissue and a surface of a matrix mixture, and (b) a dose to bedelivered to the target tissue, determining, by a processor, an activityconcentration of the radioisotope to be combined with the matrixmaterial to form the mixture. In some methods, the mixture is configuredsuch that when placed in the vertebra and when a closest surface of themixture is at the distance away from the target tissue, the mixturedelivers substantially the dose to the target tissue independently of atotal volume of the mixture placed in the vertebra. In certain methods,when the distance is about 3.4 mm, emissions from the radioisotopereaching the target tissue are emitted from substantially only withinabout 1.0 mm to about 2.5 mm of the closest surface.

Some methods for treating a bone tumor of a patient include determininga distance between the bone tumor and volume of bone cement to bepositioned within the patient and, based on at least one dose-to-depthparameter for a radioisotope, determining an activity concentration of aradioactive material to deliver radiation to the bone tumor. In somemethods, the tumor resides at the distance from an edge of the volume ofbone cement. Some methods further include outputting the activityconcentration to a nontransitory computer-readable medium. In somemethods, the edge comprises a closest edge of the matrix material to thetarget tissue.

Some methods for limiting radiation damage while treating a target witha radioisotope described herein include determining a distance between(a) a tissue to be spared radiation damage and (b) a surface of a bonecement to be positioned near the target; based on the determineddistance and based on a maximal dose of radiation to the tissue,determining an activity of the radioisotope to be mixed with the bonecement to obtain an activity concentration that limits a dose ofradiation to the tissue to less than the maximal dose; and mixing theradioisotope with the bone cement.

Some methods for treating a bone tumor of a patient include the step of,based on (i) a distance between the bone tumor and volume of bone cementto be positioned within the patient, and (ii) at least one dose-to-depthparameter for a radioisotope, determining an activity concentration of aradioactive material to deliver radiation to the bone tumor, the tumorresiding at the distance from an edge of the volume of bone cement. Somemethods include dispensing the bone cement, having the activityconcentration, to a health care worker for delivery to the patient.

In some methods for treating a target tissue with a radioisotope, themethods include mixing a radioisotope uniformly in a matrix material,the material configured to attenuate emissions of the radioisotope suchthat therapeutic emissions sufficient to treat the target tissue areemitted from substantially only the surface of the matrix material. Somemethods further include exposing the target tissue to a radioactive dosethat is delivered by the radioisotope substantially only about thesurface of the matrix material.

In some methods, an activity per unit volume of the matrix material isused to determine the dose to the target. Some methods provide that anactivity concentration and a distance from the surface of the materialare used to determine the dose delivered to the target tissue. In somemethods, the matrix material comprises polymethylmethacrylate. In somemethods, the radioisotope is a beta-emitter, and in some embodiments,the radioisotope is at least one of P-32, Y-90, and Sr-89. Some methodsprovide that the matrix material comprises a high atomic number materialthat has been mixed with a gamma-emitting radioisotope.

Some methods described herein are directed to treating a target tissuewith a radioisotope. The methods can include determining a distancebetween a target tissue and a surface of a bone cement to be positionedadjacent the target tissue; based on the determined distance and basedon a target dose of radiation to the target tissue, determining anactivity of the radioisotope to be mixed with a volume of the bonecement to obtain a desired activity concentration of the radioisotope;and mixing the radioisotope with the bone cement.

In some methods described herein for treating a target tissue with aradioisotope, the methods include determining a distance between atarget tissue and a surface of a bone cement to be positioned adjacentthe target tissue; based on the determined distance and based on atarget dose of radiation to the target tissue, determining an activityof the radioisotope to be mixed with a volume of the bone cement toobtain a desired activity concentration of the radioisotope; and mixingthe radioisotope with the bone cement.

In certain methods described herein for treating a bone tumor of apatient, the methods include determining a distance between the bonetumor and a surface of a bone cement to be positioned within thepatient; based on the distance and based on a target dose of radiationto the tumor, determining an activity concentration of the radioisotopeto deliver radiation to the bone tumor; and outputting the activityconcentration to a nontransitory computer-readable medium.

Some methods for treating a bone tumor of a patient include based on (i)a distance between the bone tumor and a surface of bone cement to bepositioned within the patient, and (ii) a dose of radiation emitted froma radioactive material, determining an activity concentration of theradioactive material that delivers the dose to the bone tumor; anddispensing the bone cement, having the activity concentration, fordelivery to the patient.

In certain methods for limiting radiation damage while treating a targetwith a radioisotope, the methods include determining a distance between(a) a tissue to be spared radiation damage and (b) a surface of a bonecement to be positioned near the target; based on the determineddistance and based on a maximal dose of radiation to the tissue,determining an activity of the radioisotope, to be mixed with the bonecement, that limits a dose of radiation to the tissue to less than themaximal dose; and mixing the radioisotope with the bone cement.

Some methods described herein for limiting radiation damage whiletreating a target with a radioisotope include determining a distancebetween (a) tissue to be spared within 10 mm of the bone tumor and (b) asurface of a bone cement to be positioned within the patient; based onthe determined distance and based on a maximal dose of radiation to thetissue, determining an activity concentration of the radioisotope, inthe bone cement, that limits a dose of radiation to the tissue to lessthan the maximal dose; and outputting the activity concentration to anontransitory computer-readable medium.

In some methods for treating a target tissue with a radioisotope, themethods include mixing a radioisotope in a matrix material, the materialconfigured to attenuate emissions of the radioisotope such thattherapeutic emissions sufficient to treat the target tissue are emittedfrom substantially only within about 1.9 mm of a surface of the matrixmaterial; and exposing the target tissue to a radioactive dose that isdelivered by the radioisotope substantially only about the surface ofthe matrix material. In some methods for treating a target tissue with aradioisotope, the methods include mixing a radioisotope in a matrixmaterial, the mixture configured to attenuate emissions of theradioisotope such that therapeutic emissions sufficient to treat thetarget tissue are emitted from substantially only within about 1.0 toabout 2.5 mm of a surface of the matrix material; and exposing thetarget tissue to a radioactive dose that is delivered by theradioisotope substantially only about the surface of the matrixmaterial. In some embodiments, such as when a low-energy beta-emittingradioisotope is mixed in a matrix material, the therapeutic emissions totreat the target tissue may be emitted from less than about 1 mm fromthe surface of the material. In some embodiments, such as when agamma-emitting radioisotope is mixed in a matrix material, thetherapeutic emissions to treat the target tissue may be emitted from adepth from the surface greater than about 2.5 mm.

Some methods of treating a target tissue in a patient's body includeproviding a cement for placement within the patient's body, the cementcomprising a plurality of radioisotopes with a range of half-lives; anddelivering the cement to a target location within the patient's body,such that the target tissue is treated with a first radioisotope of theplurality, having a half-life shorter than another of the plurality, ata higher dose than a dose administered to the target tissue by anotherof the plurality.

In some methods, the radioisotope emits gamma rays. This gamma-emittingradioisotope can also have a high atomic number material. For example,the high atomic number material can include at least one of Rhenium,Iridium, Tantalum, Tungsten, Gold, and a Lanthanide series element.

In some methods, the matrix material has a high atomic number material.In some of these methods, the radioisotope can emit gamma rays, and thegamma-emitting radioisotope can have a high atomic number material. Thehigh atomic number material can includes at least one of Rhenium,Iridium, Tantalum, Tungsten, Gold, and a Lanthanide series element.

In some methods, the bone cement includes a high atomic number materialthat has been mixed with gamma-emitting radioisotopes. Some high atomicnumber materials can include, for example, Rhenium, Iridium, Tantalum,Tungsten, Gold, and a Lanthanide element. In some methods, thegamma-emitting radioisotope and the high atomic number material are thesame material. For example, Rhenium (Re) and Iridium (Ir) are high Zmaterials and Re-186 and Ir-192 have both beta and gamma emissions. Thegamma emissions from these radioisotopes may be attenuated by the Re orIr, respectively. As a result, only the gamma emissions from thematerial near the surface of the Re- and/or Ir-laden cement would reachthe target, so the dose to the target would be relatively independent ofthe amount of radioactive cement material is administered. In somemethods, elements in the Lanthanide series can also work. For example,Sm-153, in its solid form could be used. These elements have even higherZ. As the Z is greater, the attenuation increases, and the thicknessfrom which the gamma radiation irradiation contributes to the dosedecreases.

In some embodiments, radioactive particles and flakes of a materialhaving a high atomic number can be mixed with a liquid cement thatcures. This liquid cement, with the high atomic number radioactivematerial, can be injected into a patient to treat tumors using dosimetryprinciples discussed herein.

Some embodiments include a radioactive material, for treating targettissue in a patient's body, that include a cement for placement withinthe patient's body; and a beta-emitting radioisotope mixed in the cementat a concentration of about 4 mCi per ml of cement; wherein, when anyvolume of the radioactive material is placed about 6 mm or more from anon-target tissue, the non-target tissue will be exposed to less thanabout 30 Gy; and wherein a volume of the radioactive material contactingthe target tissue delivers more than 30 Gy to a depth of up to about 3.5mm into the target tissue.

Some methods include providing a matrix material for placement withinthe patient's body, the matrix material comprising a plurality ofradioisotopes with a range of half-lives; and delivering the matrixmaterial to a target location within the patient's body, such that thetarget tissue is treated with a first radioisotope of the plurality,having a half-life shorter than another of the plurality. Some suchmethods include mixing at least one of Y-90, P-32, and Sr-89 with thematrix material. In some embodiments, methods further include mixing atleast one material having a high atomic number in the plurality ofradioisotopes. In some such embodiments, the radioisotope can emit gammarays, and the gamma-emitting radioisotope can have a high atomic numbermaterial. The high atomic number radioisotope can include at least oneof Rhenium, Iridium, Tantalum, Tungsten, Gold, and a Lanthanide serieselement. In some embodiments, methods employing a plurality ofradioisotopes can include a mixture of beta and gamma emittingradioisotopes.

In some methods of treating a vertebral tumor, the methods includeproviding a bone cement and a radioisotope to be mixed with the cementto form a mixture, having an activity concentration of the radioisotope,to be placed in a vertebra; wherein the activity concentration is basedon (a) a distance between a target tissue and a surface of a mixturewhen placed in the vertebra, and (b) a dose to be delivered to thetarget tissue. In some embodiments, the mixture is configured such thatwhen placed in the vertebra and when a closest surface of the mixture isat the distance away from the target tissue, the mixture deliverssubstantially the dose to the target tissue independently of a totalvolume of the mixture placed in the vertebra

Some embodiments include a radioactive material for treating targettissue in a patient's body, the radioactive material including a cementfor placement within the patient's body; and a beta-emittingradioisotope mixed in the cement at a concentration of up to about 100mCi per ml of cement; wherein, when a volume of the radioactive materialis placed within 5 mm of the target tissue, the dose distribution in thetarget tissue is substantially the same for any volume of theradioactive material greater than about 10 mm in diameter. In someembodiments, when any volume of the radioactive material greater thanabout 1 to about 3 mm thick, measured in the direction of the radiationemissions to the target, and greater than about 6 mm perpendicular tosaid direction, is placed near the target tissue, the depth-dosedistribution in the target tissue near the closest surface of theradioactive volume is substantially the same.

In some embodiments, a radioactive material for treating a target in apatient's body includes a cement having a density; and a beta-emittingradioisotope mixed with the cement at a concentration of up to about 100mCi per ml of cement; wherein, when a volume of the radioactive materialis placed within 10 mm of the target, the dose distribution in thetarget is substantially the same for any volume of the radioactivematerial having a thickness, in a direction of radiation emission fromthe radioactive material to the target, greater than a thresholdinversely related to the density; wherein, when the threshold is about1.8 mm, the density is about 1.35 gm/cc. In some embodiments, when thethreshold is about 1.9 mm, the density is about 1.3 gm/cc.

Some methods include determining an activity concentration of aradioisotope in a mixture for treating a target tissue in a vertebra,the method comprising based on (a) a distance between the target tissueand a surface of the mixture, and (b) a dose of radiation to bedelivered to the target tissue by the radioisotope, determining, by aprocessor, an activity concentration of the radioisotope in the mixture,the mixture resulting from combining a matrix material and theradioisotope, wherein the mixture is configured such that when placed inthe vertebra and when a closest surface of the mixture is at thedistance away from the target tissue, the mixture delivers substantiallythe dose to the target tissue independently of a total volume of themixture placed in the vertebra.

Some methods include determining a distance from a radioisotope mixtureto a target tissue in or near a vertebra, the method comprising based on(a) an activity concentration of the radioisotope in the mixture, themixture resulting from combining a matrix material and the radioisotope,and (b) a dose of radiation to be delivered to the target tissue by theradioisotope, determining, by a processor, a distance between the targettissue and a surface of the mixture, wherein the mixture is configuredsuch that when placed in the vertebra and when a closest surface of themixture is at the distance away from the target tissue, the mixturedelivers substantially the dose to the target tissue independently of atotal volume of the mixture placed in the vertebra.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts radial depth-dose curves in connection with embodimentsdescribed herein.

FIG. 2 depicts radial depth-dose curves in connection with embodimentsdescribed herein.

FIG. 3 depicts radial depth-dose curves in connection with embodimentsdescribed herein.

FIG. 4 illustrates effect of cement thickness on dose distributions inaccordance with embodiments herein.

FIG. 5 depicts dose distributions for various radionuclides potentiallyused in radioactive cement, where each dose distribution has beenadjusted to deliver 45 Gy to bone 3.5 mm from a surface of a cement.

FIG. 6 is an image of a transverse and a coronal cross-section of avertebra, showing outlines of the cubic volumes of radioactive bonecement that were modeled in each of seven MCNP models, and the voxels inwhich dose was determined.

FIG. 7 depicts distributions of dose per total initial activity for theseven MCNP models containing various sizes of cubes of radioactive bonecement.

FIG. 8 depicts distributions of dose per initial activity concentrationfor the seven MCNP models containing various sizes of cubes ofradioactive bone cement.

FIG. 9 depicts a transverse cross-section of the vertebra, showingoutlines of three-dimensional hexahedrons of radioactive bone cement, ofwhich one dimension was varied, and the voxels in which dose wasdetermined.

FIG. 10 depicts distributions of dose per initial activity concentrationfor the five MCNP models containing hexahedrons of radioactive bonecement with a 15 mm×15 mm face in the coronal plane and various anteriordepths.

FIG. 11a depicts distributions of dose per initial activityconcentration for the six MCNP models containing hexahedrons ofradioactive bone cement with a 15 mm×15 mm face in the sagittal planeand various lateral widths.

FIG. 11b depicts a plot of dose and percent change in dose per percentchange in volume as a function of cement cylinder volume at a fixeddistance from the surface of each cement cylinder.

FIG. 11c depicts a plot of dose and percent change in dose per percentchange in volume as a function of cement sphere volume at a fixeddistance from the surface of each cement sphere.

FIG. 11d depicts a plot of dose and percent change in dose per percentchange in volume as a function of cement cube volume at a fixed distancefrom the surface of each cement cube.

FIG. 11e depicts a plot of dose as a function radioactive source volume,at a fixed distance, for air and for bone cement as matrix materials.

FIG. 11f depicts a plot of percent change in dose per percent change involume as a function radioactive source volume, at a fixed distance, forair and for bone cement as matrix materials.

FIG. 11g depicts a plot of dose as a function radioactive source volume,at a fixed distance, for various matrix materials.

FIG. 11h depicts a plot of percent change in dose per percent change involume as a function radioactive source volume, at a fixed distance, forvarious matrix materials.

FIG. 12 depicts distributions of dose per initial activity concentrationfor the eight MCNP models containing a 15-mm cubic volume of radioactivebone cement with surrounding bone modeled as a uniform distribution ofvarious bone materials.

FIG. 13 depicts distributions of dose per initial activity concentrationfor the eight MCNP models containing a 15-mm cubic volume of radioactivebone cement with surrounding bone modeled as a uniform distribution of amaterial with a specific atomic composition and various densities.

FIG. 14 depicts distributions of dose per initial activity concentrationfor the eight MCNP models containing a 15-mm cubic volume of radioactivebone cement with surrounding bone modeled as a uniform distribution of amaterial with a specific density and various atomic compositions.

FIG. 15 depicts distributions of dose per initial activity concentrationfor the two MCNP models containing a 15-mm cubic volume of radioactivebone cement with either a pure P-32 radioactive source or aP-32/Ca-47/Sc-47 radioactive compound source.

FIG. 16 depicts distributions of dose per initial activity concentrationfor the four MCNP models containing a 15-mm cubic volume of P-32uniformly distributed within various bone cement types.

FIG. 17 depicts an image of coronal slots posterior to a cylindricalhole and sagittal slots lateral to the cylindrical hole, in either orboth directions.

FIG. 18 depicts images showing transverse cross-sections of a modeledvertebra.

FIG. 19 is an image showing pieces of radiochromic film cut to size,labeled and placed within the coronal and sagittal slots that had beenpreviously cut in the vertebral body.

FIG. 20 is an image illustrating that an isodose contour plot of thepredicted dose distribution exhibits an axisymmetric distribution aboutthe cylindrical radioactive cement source.

FIG. 21 depicts plots of predicted and measured radial depth-dose curvesfor two different specimens.

FIG. 22 depicts predicted and measured log-linear depth-dose curves forthe specimens.

FIG. 23 is an image illustrating open trabecular pores in one specimen,a result of marrow loss that occurred during experimental specimenpreparation.

FIG. 24 depicts predicted and measured log-linear depth-dose curves formodified MCNP models of two specimens

FIG. 25 shows depth-dose curves for a vertebral body with a 15-mm cubicvolume of radioactive bone cement indicate that the dose rapidlydecreases with distance from the surface of the cement, and thedifference between curves for a typical bone density and for bonemarrow.

FIG. 26 is a schematic of dosimetry procedure to be performed usingtransverse images through the vertebral body.

DETAILED DESCRIPTION

For purposes of summarizing the disclosure, certain aspects, advantages,and novel features of the disclosure are described herein. It is to beunderstood that not necessarily all such advantages may be achieved inaccordance with any particular embodiment of the disclosure. Thus, thedisclosure may be embodied or carried out in a manner that achieves oroptimizes one advantage or group of advantages as taught herein withoutnecessarily achieving other advantages as may be taught or suggestedherein.

Additionally, although embodiments of the disclosure have been describedin detail, certain variations and modifications will be apparent tothose skilled in the art, including embodiments that do not provide allthe features and benefits described herein. It will be understood bythose skilled in the art that the present disclosure extends beyond thespecifically disclosed embodiments to other alternative or additionalembodiments and/or uses and obvious modifications and equivalentsthereof. Moreover, while a number of variations have been shown anddescribed in varying detail, other modifications, which are within thescope of the present disclosure, will be readily apparent to those ofskill in the art based upon this disclosure. It is also contemplatedthat various combinations or subcombinations of the specific featuresand aspects of the embodiments may be made and still fall within thescope of the present disclosure. Accordingly, it should be understoodthat various features and aspects of the disclosed embodiments can becombined with or substituted for one another in order to form varyingmodes of the present disclosure. Thus, it is intended that the scope ofthe present disclosure herein disclosed should not be limited by theparticular disclosed embodiments described herein.

Disclosed herein are various embodiments related to methods ofdelivering radiation therapy to a target. It will be understood by theskilled artisan that such radioisotopes may comprise any knownradioisotope, including, without limitation, any beta emitter, anycombination of beta emitters, any gamma emitter, any combination ofgamma emitters, and any mixture of one or more beta emitters with one ormore gamma emitters.

Spinal metastases are a common and serious manifestation of cancer, andare often treated with vertebroplasty/kyphoplasty followed by externalbeam radiation therapy (EBRT). As an alternative, a radioactive bonecement, i.e. bone cement incorporated with a radionuclide, can beintroduced. Using a Monte Carlo radiation transport modeling method,dose distributions within vertebrae containing radioactive cement(phosphorus-32 radioactive bone cement) can be evaluated. Suchevaluation of vertebrae containing radioactive cement has shown thiscement to be clinically useful for treating spinal metastases. Modelaccuracy was evaluated by comparing model-predicted depth-dose curves tothose measured experimentally in eight cadaveric vertebrae usingradiochromic film. The high-gradient regions of the depth-dose curvesdiffered by radial distances of 0.3-0.9 mm, an improvement over EBRTdosimetry accuracy. The low-gradient regions differed by 0.033-0.055Gy/h/mCi, which may be important in situations involving prior spinalcord irradiation. Using a more rigorous evaluation of model accuracy,four models predicted the measured dose distribution within theexperimental uncertainty, as represented by the 95% confidence intervalof the measured log-linear depth-dose curve. The remaining four modelsrequired modification to account for marrow lost from the vertebraeduring specimen preparation. However, the accuracy of the modified modelresults indicated that, when this source of uncertainty is accountedfor, this modeling method can be used to predict dose distributions invertebrae containing radioactive cement.

According to the teachings herein, the two steps of the conventionaltreatment approach may be combined into a single procedure utilizingradioactive bone cement, i.e. bone cement incorporated with a uniformdistribution of a radionuclide. Such a combined approach would integrateradiation therapy and the surgical strength-restoration procedure into asingle procedure for treatment. This combined approach can reduce oreliminate having separate radiation therapies and as many as 10-15visits to the hospital (in the case of EBRT) for a patient whose qualityof life has already been compromised. Additionally, by directingradioactive bone cement to the location of the tumor, a beta-emittingradionuclide can be used to create emissions that penetrate only theadjacent bone/tumor, potentially allowing for a higher dose to thetarget bone and minimal dose to the spinal cord and other normal tissuenearby.

To evaluate feasibility and to guide development of the radioactive bonecement technology, an analytical tool predicts the radiation dosedistribution within and adjacent to vertebrae containing radioactivebone cement. Previously, a Monte Carlo model of a vertebra containing acylinder of radioactive bone cement was presented. Although thisvoxelized, CT scan-based model represented the vertebral geometry well,model generation was complex, limiting the usefulness of this approach.Subsequently, another study presented the dose distribution fromradioactive bone cement in a simplified model that consisted only ofcortical bone. Neither study attempted to experimentally evaluate modelaccuracy.

Described herein is a method for automatically generating anatomicallycorrect, patient-specific, CT scan-based Monte Carlo radiation transportmodels of vertebrae containing radioactive bone cement, to predict theradiation dose distribution in a vertebral body injected withradioactive bone cement. Model accuracy has been experimentallyevaluated and demonstrated to accurately predict the resulting radiationdose distributions. Thus, this modeling method provides a usefulanalytical tool with which to evaluate the clinical usefulness of thedose distributions resulting from radioactive bone cement.

Model results indicate that a therapeutic dose could be delivered totumor and bone within about 5 mm of the cement surface, whilemaintaining a safe dose to radiosensitive tissue, such as the spinalcord, beyond this distance. This therapeutic range should be sufficientto treat target volumes within the vertebral body when tumor ablationtechniques are used to create a cavity into which the radioactive cementcan be injected. Additionally, the effect of the vertebral bone densityon the resulting dose distributions was analyzed and determined to benegligible for physiologic ranges of trabecular bone density within thevertebral body. Thus, with further development, radioactive bone cementmay become an alternative to the conventional two-step approach(percutaneous strength-restoration procedure followed by radiotherapy)to treating spinal metastases.

Further embodiments describe different embodiments of various dosedistributions resulting from radioactive bone cement. The clinicalusefulness of these dose distributions is characterized, in someembodiments, by the attenuation of dose with distance from the cement,as well as the therapeutic range, maximum dose to bone, and dose to thespinal cord for various levels of implanted activity. The effect of thevertebral bone density on the radioactive cement dose distributions wasalso analyzed, as explained below.

The CT scan-based Monte Carlo radiation transport modeling method wasused to evaluate dose distributions from radioactive bone cement. Modelswere also used to predict and compare dose distributions in a vertebrawith its actual heterogeneous distribution of bone density, as well asuniform distributions of various bone densities.

The T12 vertebra was acquired for the model from a 69-year-old femaledonor who died from anoxic encephalopathy. A silicone mold of theposterior element of the vertebra was created and used to hold thespecimen in place during CT scanning, and CT scans were obtained withthe vertebra immersed in water to minimize streak artifacts (GEDiscovery VCT PET/CT, standard reconstruction, 0.625-mm pixel size,1.25-mm slice thickness, 80 kVp, 280 mAs). A calcium hydroxyapatitecalibration phantom (Image Analysis Inc., Columbia, Ky.) was included ineach scan and used to calculate the quantitative CT density (ρ_(QcT)) ofeach pixel.

In-house software was used to transform the CT scan data into a MonteCarlo N-Particle (MCNP) model consisting of a three-dimensionalrectangular lattice of 0.625 mm×0.625 mm×1.25 mm voxels. All bone in themodel was assigned a material number according to ρ_(QCT) of thecorresponding CT voxel. Each bone material was defined by its densityand atomic composition and represented one of thirty complementaryvolume fractions of solid cortical bone and marrow. All soft tissue inthe model, including the spinal cord, muscle, and fat, was representedby a single material. A 1.19 cm-diameter×1.13 cm-height cylindricalvolume of ArthroCare Parallax® PMMA bone cement (ArthroCare Corp.,Sunnyvale, Calif.) was simulated within the model, replacing trabecularbone at the approximate center of the vertebral body. A phosphorus32(P-32) radionuclide source was modeled as uniformly distributed withinall cement voxels, with the complete energy spectrum from MedicalInternal Radiation Dose (MIRD) data. P-32 was selected due to itshigh-energy beta emissions (maximum: 1.71 MeV), clinically-relevanthalf-life (14.3 days), prior use as a radiopharmaceutical for painpalliation in patients with bone metastases, and because model accuracywas previously validated for P-32 as the radionuclide. Although thisanalysis was carried out using P-32, in alternate embodiments, methodsof the invention may employ other radioisotopes, including, withoutlimitation, other beta emitters, gamma emitters, and mixtures thereof.One skilled in the art will recognize that the specific numericalresults of MCNP models employing other radioisotopes may differ fromthose described herein.

Thirty million particle histories were simulated (MCNPX v.2.5.0, LosAlamos National Laboratory, LANL) using the default cross-sections. Thedose distribution was assumed to be axisymmetric about the cylindricalradioactive cement source, and pulse-height energy distribution tallieswere averaged over four radial directions (anterior, posterior, leftlateral, right lateral) within each of three consecutive transverseplanes near the center of the height of the cement cylinder. The dosedistribution was characterized by a radial depth-dose curve, i.e., theabsorbed dose (Gy) over the lifetime of the radionuclide, for 1 mCi (37MBq) of initial activity, versus radial distance from the surface of theradioactive cement, with tally results assumed to be at the center ofeach voxel.

The radial depth-dose curve was analyzed to evaluate the clinicalusefulness of the dose distribution. The curve was first used tocharacterize the attenuation of dose with distance from the radioactivesource, represented by the distance from the cement at which theabsorbed dose was attenuated to 10% and 1% of the maximum absorbed dosein the voxel directly adjacent to the cement (R_(10%) and R_(1%),respectively).

Since the dose distribution linearly scales according to the amount ofinitial activity, radial depth-dose curves were then also plotted forinitial activities of 2, 4, 8, and 16 mCi (74, 148, 296, and 592 MBq,respectively). For each initial activity, the resulting radialdepth-dose curve was used to quantify the radial distance at which atherapeutic dose (38 Gy) is delivered (R_(TD)); the maximum absorbeddose in the voxel directly adjacent to the cement (D_(Max)); the radialdistance at which the maximum allowable dose to the spinal cord (54 Gy)is delivered (R_(cord)); and the absorbed dose at the anterior surfaceof the spinal canal, corresponding to a radial distance of 7 mm from thecement (D_(7 mm)).

To demonstrate how changes in the vertebral bone density affect the dosedistribution from radioactive bone cement, nine MCNP models were createdin which all bone in the vertebra was modeled as a uniform distributionof a single bone material. To accomplish this, the model described abovewas modified such that all thirty bone material definitions consisted ofthe same density and atomic composition, while the model geometry, softtissue material definition, radioactive cement source, and tallies allremained the same. Models with a uniform distribution of bone densitywere created using the bone densities and corresponding volume fractionsof marrow and cortical bone shown in Table 1.

TABLE 1 Model Bone Density Volume fractions (%) ID (g/cm³) Marrow BoneB01 0.980 100 0 B06 1.104 89.8 10.2 B13 1.221 80.2 19.8 B18 1.369 68.131.9 B21 1.497 57.6 42.4 B23 1.606 48.7 51.3 B25 1.738 37.9 62.1 B271.897 24.9 75.1 B30 2.200 0 100

Note that these densities are true bone densities, accounting for boneas well as marrow within its pores, and not bone mineral densities. Foreach model, the resulting radial depth-dose curve was normalized to themaximum absorbed dose in the voxel directly adjacent to the cement. Theeffect of the surrounding bone density on the radiation dosedistributions was then quantified by estimating R_(10%) and R_(1%) foreach normalized radial depth-dose curve.

For the model with the CT scan-based, heterogeneous distribution of bonedensity, the lifetime dose per mCi of initial activity is shown in FIG.1 on a linear (left) and log (right) scale. The secondary y-axis of eachplot indicates the values on the primary y-axis normalized to themaximum absorbed dose in the voxel directly adjacent to the radioactivecement. The radial depth-dose curve decreases exponentially withincreasing distance from the radioactive cement. The radial depth-dosecurve for the model with the actual, CT scan-based, distribution of bonedensity demonstrated that the lifetime dose per mCi of initial activitydecreases exponentially with increasing distance from the radioactivecement, yielding an R_(10%) and R_(1%) of 2.5 mm and 4.2 mm,respectively.

In addition to the radial depth-dose curve for an initial activity of 1mCi, above, the radial depth-dose curves for initial activities of 2, 4,8, and 16 mCi (74, 148, 296, and 592 MBq, respectively) wereconstructed, with the therapeutic dose of 38 Gy also indicated. For themodel with the CT scan-based, heterogeneous distribution of bonedensity, the lifetime dose for various initial activities is shown inFIG. 2 on a linear (left) and log (right) scale. For reference, thetherapeutic dose of 38 Gy is also shown on the log scale plot. Thecorresponding R_(TD) ranged from 3.5-5.1 mm; the corresponding D_(Max)ranged from 1445-23119 Gy; the corresponding R_(cord) ranged from3.2-5.0 mm; and the corresponding D_(7 mm) ranged from 0.10-1.56 Gy, asshown below in Table 2, which shows dosimetric characteristics of theradial depth-dose curve for the model with actual bone densitydistribution using various initial activities.

TABLE 2 Initial R_(TD) D_(Max) R_(cord) D_(7 mm) Activity (mm) (Gy) (mm)(Gy)  1 mCi  37 MBq 3.5 1445 3.2 0.10  2 mCi  74 MBq 4.0 2890 3.8 0.19 4 mCi 148 MBq 4.4 5780 4.2 0.39  8 mCi 296 MBq 4.8 11559 4.6 0.78 16mCi 592 MBq 5.1 23119 5.0 1.56

For each model with a uniform distribution of bone density, theresulting radial depth-dose curve, normalized to the maximum absorbeddose in the voxel directly adjacent to the cement demonstrated that forthese models, R_(10%) and R_(1%) were between 1.5-2.7 mm and 2.4-4.5 mm,respectively, as shown in Table 3, which shows attenuationcharacteristics of the radial depth-dose curve for each model with auniform distribution of bone density.

TABLE 3 Model ID R_(10%) (mm) R_(1%) (mm) B01 2.7 4.5 B06 2.4 4.1 B132.3 3.7 B18 2.1 3.4 B21 1.9 3.2 B23 1.8 3.0 B25 1.7 2.8 B27 1.6 2.6 B301.5 2.4

The clinical usefulness of dose distributions from P-32 radioactive bonecement was examined by determining the therapeutic range, maximum dose,and dose to the spinal cord of these dose distributions. The results ofthis study indicate that these dose distributions could be used todeliver a therapeutic dose to a clinically useful distance withinvertebrae with spinal metastases, while maintaining a safe dose to thespinal cord. As mentioned above, although this analysis was carried outusing P-32, in alternate embodiments, methods of the invention mayemploy other radioisotopes, including, without limitation, other betaemitters, gamma emitters, and mixtures thereof. One skilled in the artwill recognize that the specific numerical results of MCNP modelsemploying other radioisotopes may differ from those described herein.

For the initial model with the CT scan-based heterogeneous distributionof bone density, the absorbed dose is attenuated exponentially withdistance from the cement. The steep gradient of this dose distributionresults in a highly-localized dose and minimal exposure to nearbyradiosensitive tissues, a result that would be difficult or impossibleto achieve with a gamma-emitting radionuclide. Conversely, the gradientis flat enough that 10% of the maximum dose is delivered to bone within˜2.5 mm and 1% of the maximum dose is delivered within ˜4.2 mm. Thisresult might be difficult, or less-likely, to achieve with analpha-emitting or low-energy beta-emitting radionuclide, which wouldlikely produce emissions that may be completely absorbed by boneimmediately adjacent to the cement. These attenuation characteristicsindicate that the dose distributions from P-32 radioactive cement may beclinically useful. It was also noted that the dose distribution linearlyscales according to the amount of initial activity.

The therapeutic range of the dose distribution increases by 0.3-0.5 mmfor every doubling of the initial activity. However, considering thatD_(Max) also doubles with each doubling of the initial activity(discussed below), the practical limit on the level of implantedactivity is likely between 10-20 mCi (370-740 MBq), yielding a maximumtherapeutic range for P-32 radioactive bone cement of about 5 mm. Theclinical usefulness of this distance would be dependent on the accuracywith which the cement could be placed near the target volume within thevertebra. This issue is slightly complicated by the fact that the targetvolume used in SBRT for spinal metastases is not yet standardized,ranging from only the identifiable extent of the tumor to the entirevertebra, including the pedicles and posterior elements.

Injection of bone cement directly into a lesion has been shown to fillmore than 75% of the tumor volume with cement. For a target volumeconsisting of only the identifiable extent of the tumor, injectingradioactive bone cement directly into the tumor would likely deliver atherapeutic dose to most or all of the target volume. However, since thetumor tissue acts as an incompressible space-occupier, extensive fillingof the tumor itself also leads to increased risk of cement and/or tumorextravasation into the spinal canal. Thus, embodiments of tumor removalor ablation techniques, such as curetting, laser-induced thermotherapy,and plasma-mediated radiofrequency ablation, can be used to debulk thetumor tissue prior to cement injection, creating a cavity into which thecement can then be injected. These techniques can enable radioactivebone cement to be accurately placed directly in the target volume,immediately adjacent to residual tumor tissue that may remain afterdebulking, and with minimal risk of cement extravasation. Thus, whenused in conjunction with these ablation techniques, radioactive bonecement with a therapeutic range of 5 mm would likely be appropriate totreat a target volume consisting of the extent of the tumor.

When used in conjunction with ablation and other cavity-creatingtechniques, radioactive bone cement may also be able to effectivelytreat target volumes beyond the extent of the tumor. These tumordebulking methods would enable the radioactive cement injection to beaccurately controlled and placed in specific locations within thevertebral body, resulting in a predictable cement fill that wouldperhaps make a therapeutic range of 5 mm sufficient to treat theentirety of even a large vertebral body. However, in the event that aregion is not adequately irradiated and/or a tumor recurs, it shouldalso be noted that prior use of radioactive bone cement would notpreclude repeating this treatment or subsequent treatment withconventional radiotherapy.

Although the therapeutic range of radioactive bone cement can beextended by increasing the initial activity, the maximum dose to bonedirectly adjacent to the cement doubles with each doubling of theinitial activity, thus presenting an upper limit to the initial activitythat can be safely implanted. The maximum doses for the initialactivities studied here might be particularly useful for treating tumorsthat are relatively insensitive to radiation, such as melanoma, renalcell, and thyroid metastases. However, absorbed doses as high as 23 kGy,as predicted in this study for an initial activity of 16 mCi, would alsobe expected to lead to bone resorption and necrosis, potentially leadingto an eventual reduction in the structural integrity of the vertebralbody. Fortunately, this effect would be mitigated by the presence of thecement itself, which would provide structural reinforcement to theaffected region. Furthermore, the compressive mechanical properties ofhuman trabecular bone become significantly degraded at doses between 51kGy and 60 kGy, above the predicted dose, so the short-term structuralintegrity of the bone surrounding the radioactive cement would be lesslikely at risk. Such high doses would also not be expected tosignificantly degrade the mechanical properties of the cement itself, asonly slight reductions result from doses as high as 100 kGy.

Finally, R_(cord) and D_(7 mm) can be used to determine whetherradioactive bone cement would deliver excessive radiation toradiosensitive tissues such as the spinal cord. Values of R_(cord) forthe initial activities studied here indicate that the radioactive cementcould not be safely placed within 3-5 mm of the spinal cord, similar tothe 5 mm margin between tumor and spinal cord used in SBRT. In thisparticular model, where the anterior surface of the spinal canal is 7 mmaway from the surface of the radioactive cement, the absorbed doses(D_(7 mm)) are much lower than the maximum allowable dose to the spinalcord, even for the highest level of initial activity. Thus, even inpatients with prior spinal cord irradiation, the absorbed dose at thisdistance would be unlikely to cause spinal cord myelopathy.

For four of the models with a uniform distribution of bone density, theradial depth-dose curve, normalized to the maximum absorbed dose in thevoxel directly adjacent to the radioactive cement, is shown in FIG. 3 ona linear (left) and log (right) scale. Curves of FIG. 3 indicate thatthe dose from radioactive bone cement is attenuated more rapidly byhigher density bone than lower density bone. This effect may be oflittle importance when the functional range of the dose distribution iscompletely confined within the interior of the vertebral body, whichconsists of trabecular bone with a comparatively narrow density range.For three female and six male donors between the ages of 44-88 years,the density (with marrow) of vertebral trabecular bone was between1.0-1.1 g/cm³. The differences between R_(10%) and R_(1%) on the radialdepth-dose curves for bone densities of 0.980 g/cm³ (model B01) and1.104 g/cm³ (model B06) was 0.3 mm and 0.4 mm, respectively, indicatingthat the sensitivity of the dose to realistic variations in trabecularbone density is negligible. However, presence of blastic lesions mayincrease attenuation of the radiation and reduce the dose. Further, theincreased attenuation of high density bone might be beneficial forshielding the spinal cord and nerves, as the cortical shell wouldprovide additional attenuation of the radiation dose as it exits thevertebral body. For the model of solid cortical bone (with a density of2.200 g/cm³), our values for R_(10%) and R_(1%) (1.5 mm and 2.4 mm,respectively) are similar to an other researcher's estimates for R_(10%)and R_(1%) of 1.03 mm and 2.00 mm, respectively. These results comparewell after considering that our tally results were assumed to be at thecenter of each voxel, while other calculations assume tally results tobe at the edge closest to the cement, leading to an offset in the radialdistance of 0.3125 mm.

This study evaluated dose distributions resulting from radioactive bonecement using P-32 as the radionuclide. Alternative radionuclides such asstrontium-89 (Sr-89), yttrium-90 (Y-90), and rhenium-188 (Re-188), eachwith their own characteristic energy spectrum and particle emissionstype, would produce dose distributions that might vary greatly fromthose presented here. Using these radionuclides in combination may alsoprovide some benefits by taking advantage of varying half-lives andparticle energies. The MCNP models can be easily modified to predictdose distributions from alternative radionuclides or combinationsthereof. However, an experimental evaluation of model accuracy, as wasperformed previously for P-32, would be carried out when employingalternative radionuclides. Thus, methods of the invention may includeany mixture of Y-90, P-32, and Sr-89. In some embodiments, methods mayalso include at least one radioisotope having a high atomic number. Insome such embodiments, the radioisotope can emit gamma rays, and thegamma-emitting radioisotope can have a high atomic number. The highatomic number radioisotope can include at least one of Rhenium, Iridium,Tantalum, Tungsten, Gold, a Lanthanide series element, and mixturesthereof. In some embodiments, methods employing a plurality ofradioisotopes can include a mixture of beta and gamma emittingradioisotopes.

Dose distributions were evaluated using an idealized, cylindrical volumeof radioactive bone cement. Clinical vertebroplasty may involve cementdistributions that are more complex and involve cement-boneinterdigitation. However, the cylindrical cement specimens enabled theirresulting axisymmetric dose distributions to be quantified by a singleradial depth-dose curve, greatly simplifying their characterization anddosimetric analysis. Use of the idealized cement geometry also allowedthe surrounding bone density to be easily modified, enabling asystematic analysis of its effect on the resulting dose distribution.

Since extravasation of radioactive bone cement into the spinal canalcould lead to an extremely high dose to the spinal cord, use ofradioactive bone cement with tumor ablation techniques may be advisable.Additionally, the cement viscosity at the time of injection could affectthe likelihood of extravasation, and guidelines for injecting at theoptimal viscosity may thus be developed.

Although systemic uptake of a liquid radionuclide has been used inconjunction with kyphoplasty, it is desirable for leaching of theradionuclide from the cement be prevented to minimize toxicity inradiosensitive tissues outside of the vertebra. This issue is dependenton the chemical form of the radionuclide.

Dose distributions from P-32 radioactive bone cement were evaluated andshown to be clinically useful for treating spinal metastases. Modelresults indicated that a therapeutic dose could be delivered to tumorand bone within about 5 mm of the cement surface, while maintaining asafe dose to radiosensitive tissue, such as the spinal cord, beyond thisdistance. This therapeutic range should be sufficient to treat targetvolumes within the vertebral body when tumor ablation techniques areused to create a cavity into which the radioactive cement can beinjected. Additionally, the effect of the vertebral bone density on theresulting dose distributions was analyzed and determined to benegligible for physiologic ranges of trabecular bone density within thevertebral body. Thus, radioactive bone cement may be used as analternative to the conventional two-step approach (percutaneous strengthrestoration procedure followed by radiotherapy) to treating spinalmetastases.

The therapeutic dose and an upper limit of allowable dose, in someembodiments, to the spinal cord were calculated using thelinear-quadratic approach to provide doses with the same biologicaleffectiveness as the corresponding doses used in conventionalradiotherapy. For conventional radiotherapy, the biologically effectivedose (BED) is given by:

$\begin{matrix}{{BED} = {{nd}( {1 + \frac{d}{\alpha/\beta}} )}} & (1)\end{matrix}$where n and d are the number of fractions and the dose per fraction,respectively, for fractionated radiotherapy, and α/β is a characteristicof the fractionation sensitivity specific to each tissue type. For apermanent implant, the BED is given by:

$\begin{matrix}{{BED} = {D\{ {1 + \lbrack \frac{D \cdot \lambda}{( {\mu + \lambda} )( {\alpha/\beta} )} \rbrack} \}\begin{matrix}\; \\\;\end{matrix}}} & (2)\end{matrix}$where D is the total absorbed dose over the lifetime of theradionuclide, λ is the radioactive decay constant of the radionuclide,and μ is the tissue repair rate constant, assumed to be 0.46 h⁻¹.Substituting (1) into (2) results in a quadratic equation that can besolved for D, yielding the physical lifetime dose from a permanentimplant that has the same biological effectiveness as the fractionatedradiotherapy to which it is compared. For patients receiving EBRT forspinal metastases, a total dose of 30 Gy fractionated over 10 dailytreatment sessions of 3 Gy/fraction is often prescribed. Using α/β=10 Gyfor tumor control, this corresponds to a BED of 39 Gy₁₀. Likewise, forpatients receiving a single fraction of SBRT for spinal metastases, themaximum allowable dose to the spinal cord is often set at 10 Gy. Usingα/β=2 Gy for late effects in the spinal cord, this corresponds to a BEDof 60 Gy₂. For a P-32 permanent implant, these BEDs correspond tophysical lifetime doses of 38 Gy and 54 Gy for a therapeutic dose andthe maximum allowable dose to the spinal cord, respectively. That thetherapeutic dose is less than the maximum allowable dose to the spinalcord is a result of the difference between the α/β ratios used for acutetumor effects (α/β=10 Gy) and late-reacting tissues such as the spinalcord (α/β=2 Gy), as well as the half-life of P-32. The extended deliveryperiod of the P-32 radionuclide allows for more repair of late-reactingtissue than does a single, hypofractionated dose from SBRT.

Some embodiments herein relate to a characteristic of the radioactivebone cement and are in contrast with the conventional approach tobrachytherapy. In conventional brachytherapy, radioactive seeds areimplanted in or next to the tissue requiring radiation therapy (thetumor, or target, region). Since each brachytherapy seed contributes tothe dose to the target region, increasing the activity increases thedose, and treatment guidelines are developed in terms of the totalactivity implanted.

In comparison, since radioactive bone cement is intended to providestructural support in addition to radiation therapy, the volume ofcement injected depends on the size of the cavity it fills, so theentire volume of radioactive bone cement is not necessarily in closeproximity to the target region. When P-32, a radioactive isotope ofphosphorous and a beta-emitter, is used as the radioisotope, increasingthe dose to the target region is not necessarily accomplished by addingmore radioactive bone cement, since the additional bone cement may befarther away from the target region than the range of the P-32emissions. Instead, the radiation dose delivered to the target region isdependent only on the activity in the cement that is within a certainspecified distance. This distance is a characteristic of the particularradioisotope. Therefore, treatment guidelines for using radioactive bonecement with P-32 as the radioisotope should not be developed in terms ofthe total amount of cement (and, thus, the total activity) implanted inthe bone, but should instead be in terms of the activity concentrationin the cement (mCi per ml of cement). The following example illustratesthe underlying principle. If the amount of cement injected into a boneis doubled, the total activity in the bone would be doubled, but thedose to a given target region will change only when that target regionis within a certain specified distance from the additional volume ofcement.

Specific calculated values of the cement thickness beyond whichadditional cement will not increase the dose delivered to target tissue(tissue near the X and X′ axes) are illustrated in FIG. 4.

The fundamental reason that the radioactive cement demonstrates thisproperty is that beta emissions penetrate only a short distance throughpolymethylmethacrylate (PMMA). As a result, the radiation dose to targettissue, which would be near the X and X′ axes in FIG. 4, depends almostentirely on the activity of the radioactive material that is near thesurface of the bone cement. Based on computer models, the dose to targettissue from about a 2 mm thick layer of radioactive cement isessentially identical to the dose from an infinitely thick layer ofcement. This is correct if the thickness of the cement that is placed inthe tissue is greater than approximately 1.875 mm. As shown in FIG. 4,the dose distribution along axis X is the same as that along axis X′, aslong as the cements are identical. The 1.875 mm figure is for P-32.

A lower energy beta emitter would require a lower thickness (comparedwith 1.875 mm for P-32) to exhibit this behavior. In some embodiments,such as when a low-energy beta-emitting radioisotope is mixed in amatrix material, the surface thickness may be less than about 1.0 mm.The lower energy beta emitter would also not penetrate as deeply intothe surrounding tissues. This could be useful for very sensitive tissuesin which penetration is to be very short.

This characteristic is probably not true for most gamma emittingradioisotopes because gamma radiation can penetrate bone cement.However, very low-energy gamma emitters may exhibit this behavior. Insome embodiments, such as when a gamma-emitting radioisotope is mixed ina matrix material, the surface thickness may be greater than about 2.5mm. Further, for a gamma-emitting radioisotope, gamma emissions may besufficiently attenuated by a matrix material with a high atomic numberand/or a high density to cause the dose to a target tissue at a specificdistance from the cement surface to be approximately constant when thecement thickness reaches or exceeds a particular thickness.

The amount of activity that can be mixed with the cement to deliver aclinically relevant dose to the bone is feasible from a logistical,economic, and physical perspective, despite the fact that only theactivity “near the surface” of the cement influences the dose to thebone. If, say, only the cement within 0.01 mm of the surface wereresponsible for the dose to the bone, the amount of activity that wouldbe necessary to mix with the cement would be so great that it would beprohibitively expensive. Also, it is possible that, for someradioisotopes, it could be physically impossible to achieve a sufficientspecific activity (mCi per unit mass) to make a useful radioactive bonecement (e.g. if the specific activity required was too high to achievewith available nuclear reactors, and/or if the achievable specificactivity required such a great amount of radioactive compound that itwould affect the mechanical properties of the cement).

Although the disclosure throughout describes studies and methodsconducted with P-32, there may be a number of radioisotopes that can beused. For example, Sr-89 behaves much like P-32. The required activityto deliver the target dose depends on the energy (which determines thethickness through which the beta emission will pass), the half-life, andwhether the radioisotope is a gamma or beta-emitter. FIG. 5 and Table 4shows the results of preliminary models that determined the activityrequired to deliver 45 Gy to bone 3.5 mm from the surface of the cement.

TABLE 4 Half Max β- Mean β- γ γ Activity life Energy Energy EnergyEmissions Req'd Dose (Gy) Dose (Gy) Isotope (days) (MeV) (MeV) (MeV) (%)(mCl) at 0.3 mm at 7.2 mm P-32 14.3 1.709 0.695 n/a n/a 0.94 1508.4 0.0Ca-45 163.8 0.251 0.0769 0.0125 0.000003 810.38 138265.8 23.4 Ca-474.536 1.94 0.398 5.01 589.7 13.5 Sr-89 50.5 1.46 0.58 0.91 0.009 0.511241.4 14.0 Y-90 2.67 2.281 0.934 n/a n/a 1.06 440.5 0.9 Pd-103 17 0.4930.021 44.21 245.9 33.5 I-125 60.1 0.031 0.0274 10.42 205.4 39.5 Pr-1420.797 2.162 0.809 1.58 3.700 37.59 2019.9 23.7 Sm-153 1.95 0.81 0.230.103 28.000 348.94 2254.2 39.9 Re-186 3.87 1.071 0.323 0.137 9.500137.18 7768.8 30.8 Re-188 0.708 2.118 0.765 0.155 15.000 21.75 723.5 2.0

If the radioactive cement that were used did not exhibit the property ofsurface emission, methods of application would include estimating thevolume of cement that would be injected before doing the procedure andthen performing computer modeling or, perhaps, using charts to determinein advance how much activity can be mixed with the total amount ofcement that would be injected. In many instances, this approach can belogistically difficult.

Also, in many such instances, radioactive seeds, not radioactive cement,may be used. Prior to implanting the seeds, calculations can beperformed to determine the number of seeds, the activity in each seed,and placement locations in order to achieve the desired dose and dosedistribution. Increasing the number of seeds and/or the activity in eachseed would result in a greater dose. In many instances, this approachcan also be logistically difficult.

In some embodiments described herein, the desired dose is determined inconnection with the distance between the target dose and the surface ofthe cement. These parameters can be used to determine the activityconcentration (mCi per vol. of cement) that are used in the mix. In someembodiments, the amount of cement injected is not required for theadministering calculation as long as the surface of the cement ispositioned in the proper location, relative to the target, in order toobtain the desired or target dose.

A number of parametric studies were conducted to examine the sensitivityof the radiation transport modeling method to various model componentsincluding the volume/shape of the cement source, the materialdefinitions of the surrounding bone, and the specific form of theradioisotope and bone cement used. As such, these factors were adjustedindependently of the remaining model parameters to determine theireffect on the resulting dose distribution. The volume and shape of theradioactive cement source, as well as the density of the surroundingbone material, influence the resulting dose distribution within thevertebral body; while the atomic composition of the surrounding bone,the specific radioactive compounds analyzed, and the bone cement brandsanalyzed, do not. The effects of the cement volume and shape on dosedistribution may have important implications for the clinicalimplementation of radioactive bone cement to treat spinal metastases.This information will be important in the development of clinicaltreatment guidelines. The relative effects of all of the studiedparameters on the resulting dose distribution are valuable for otherparts of this study, in which the accuracy of the MCNP modeling methodwill be evaluated, and the models modified as necessary until thepredicted dose distributions agree with those measured experimentally.

The basis for the parametric studies was a CT scan-based MCNP model ofan L4 vertebra, created using the modeling method developed and with thefollowing model characteristics: three-dimensional rectangular latticeof 0.625 mm×0.625 mm×1.25 mm voxels; thirty bone materials and one softtissue material, as described previously; P-32 radioisotope sourceuniformly distributed within ArthroCare Parallax® Bone Cement(ArthroCare Corp., Sunnyvale, Calif.); pulseheight energy tallies in acolumn of voxels extending away from the center of the posterior face ofthe cement volume (FIG. 6, FIG. 9); 30 million particle histories; MCNPXv.2.5.0. The tally results were used to predict lifetime dosedistributions for each set of input parameters, thereby allowing theeffect of changes in each model parameter to be elucidated.

To understand the effect of volume of the cement source on the dosedistribution, seven Monte Carlo N-Particle (MCNP) radiation transportmodels were created of an L4 vertebra. Each model contained a cubicvolume of cement, with edge lengths ranging from 2.5 mm to 17.5 mm, in2.5 mm increments, and located within the vertebral body such that theposterior face of each cube was centered in the same position (FIG. 6).FIG. 6 depicts a transverse cross-section of the L4 vertebra from Donor1 (discussed further below, with reference to Table 5), showing outlinesof the cubic volumes of radioactive bone cement that were modeled. Ineach model, the dose distribution was analyzed in a column of bonevoxels extending away from the center of the posterior face, representedby the solid white column (FIG. 6). The analyzed voxels were the samefor each model, so observed differences were due only to changes in thevolume of the cement source. The inlay shows a coronal cross-section ofthe vertebra, viewed in the anterior direction (in the direction of thearrows), and the position of each cubic volume of cement within thecoronal plane.

The distributions of dose per mCi of total initial activity for eachvolume of cement for the seven MCNP models containing various sizes ofcubes of radioactive bone cement are shown in FIG. 7. The distributionsindicate that, if the total initial activity mixed with the cement isheld constant, a smaller volume of cement yields a greater dose to thetarget region than a larger volume of cement. This result can beattributed to the fact that the total initial activity is more highlyconcentrated in a smaller volume than a larger volume. Accordingly, itis likely that more clinically relevant information can be elucidated byanalyzing dose distributions for a constant initial activityconcentration, i.e., dose per mCi per unit volume of the cement.

FIG. 8 illustrates distributions of dose per initial activityconcentration for the seven MCNP models containing various sizes ofcubes of radioactive bone cement. The dose distributions indicate that,as the cube size increases, the dose distribution in the target regionapproaches a constant value. This result demonstrates the limited rangeof beta radiation emitted from a P-32 source and indicates that sourceparticles contribute to the dose distribution in a specific targetregion only when they originate within a certain distance from thetarget region. Subsequent analyses were performed on dose distributionsper initial activity concentration, i.e., dose per mCi per unit volumeof the cement.

The effect of cement shape on dose distribution was furthercharacterized by creating 11 additional MCNP models in which only one ofthe dimensions of a hexahedral cement volume was varied. For all models,dose per initial activity concentration (Gy/(mCi/ml)) was analyzed inthe same column of voxels as were analyzed for the cubic volumes ofcement, regardless of which dimension was being varied (FIG. 9).

FIG. 9 depicts a transverse cross-section of the L4 vertebra, showingoutlines of three-dimensional hexahedrons of radioactive bone cement, ofwhich one dimension was varied. Each hexahedron was based on the 15 mmedge-length cubic volume studied previously, with a 15 mm×15 mm face andvarious anterior depths (top) or lateral widths (bottom). Three of thefive depths (0.625, 1.875, and 3.75 mm, top, left-to-right) and three ofthe six widths (1.25, 3.75, and 6.25 mm, bottom, left-to-right) areshown. The dose distribution was analyzed in the same region in eachmodel, represented by the solid white columns.

To analyze the effect of the anterior depth of the hexahedron, thedimensions of the 15 mm×15 mm face in the coronal plane were heldconstant, and depth in the anterior direction was varied (0.625, 1.25,1.875, 2.5, and 3.75 mm) (FIG. 9, top). Illustrated in FIG. 10 aredistributions of dose per initial activity concentration for the fiveMCNP models. For depths greater than 1.875 mm, the dose distributioncurves are nearly identical (FIG. 10), indicating that there is a depthof the hexahedron beyond which additional source particles no longercontribute to the dose in the target region. This result demonstratesthe shielding effect of the cement itself, and indicates that it ismainly the source particles generated near the surface of the volumethat contribute to the target dose. Thus, only a thin layer ofradioactive cement using a beta-emitter such as P-32 may be sufficientto produce the clinically-desired dose distribution in a given region ofbone. Accordingly, some embodiments can include a first layer ofsubstantially uniform distribution of radioisotopes, and a second,internal layer that does not have the substantially uniformdistribution.

To analyze the effect of the lateral width of the hexahedron, thedimensions of the 15 mm×15 mm face in the sagittal plane were heldconstant, and width in the lateral direction was varied (1.25, 2.5,3.75, 5.0, 6.25, and 7.5 mm) (FIG. 9, bottom). FIG. 11a illustratesdistributions of dose per initial activity concentration for these MCNPmodels. For widths greater than 6.25 mm, the dose distribution curvesare nearly identical (FIG. 11), indicating that there is a width of thehexahedron beyond which additional source particles no longer contributeto the dose in the target region. This result demonstrates the range ofsource particles within the bone, as source particles generated acertain distance to either side (half the lateral width of thehexahedron) never reach the target region and do not contribute to itsdose distribution. This may be a less clinically-relevant result thanthe effect of the anterior depth of the hexahedron, since it is unlikelythat the clinical target region will be as narrow as the column ofvoxels examined here. Thus, source particles generated too far to theside of one target region will still likely contribute to the dosedistribution in adjacent target regions.

The relationship between dose and cement volume for a constant activityconcentration was further established using MCNP models of P-32radioactive bone cement surrounded by a uniform distribution of bone.The density of the surrounding bone was 1.22 g/cm³, representing typicalhuman vertebral trabecular bone. Other densities would yield analogousresults. Models were created for cylinders, spheres, and cubes ofradioactive cement, as explained in the following examples.

For cylindrical cement volumes, a cylinder height of 2 cm and diameters(d) from 2.5 mm to 30 mm were evaluated. Tallies were obtained inconcentric cylindrical shells of bone (each measuring 0.625-mm thick and2-cm tall), located concentrically about the cement cylinder. Forspherical cement volumes, diameters (d) from 2.5 mm to 30 mm wereevaluated. Tallies were obtained in concentric spherical shells of bone(each measuring 0.625-mm thick), located concentrically about the cementsphere. For cubic cement volumes, edge lengths (L) from 2.5 mm to 25 mmwere evaluated. Tallies were obtained in a layer of bone0.625-mm-thick×L×L hexahedrons placed on one face of the cement cube.

For spherical cement volumes, diameters (d) from 2.5 mm to 30 mm wereevaluated. Tallies were obtained in concentric spherical shells (eachmeasuring 0.625-mm thick), located concentrically about the cementsphere. For cubic cement volumes, edge lengths (L) from 2.5 mm to 25 mmwere evaluated. Tallies were obtained in a layer of 0.625-mm-thick×L×Lhexahedrons placed on one face of the cement cube. The density of thesurrounding bone was 1.22 g/cm³, representing typical human vertebraltrabecular bone. Other densities would yield analogous results.Moreover, although this analysis was performed for P-32, one skilled inthe art would further recognize that analogous results may be obtainedfor other beta emitters or gamma emitters.

Tally results were used to create depth-dose curves (lifetime doseversus distance from the surface of the cement volume) for each model,assuming an initial activity concentration of 1 mCi per ml of cement.Total activity is proportional to cement volume for a constant activityconcentration. The computed dose at fixed distances of 2.1875, 3.4375,and 4.0625 mm (the center of the fourth, sixth, and seventh tallies fromthe cement surface, respectively) was plotted against cement volume, andthe results for a distance of 3.4375 mm are shown in FIGS. 11b-11d .This range of distances was selected because the computed dose over thisrange approximates a therapeutic dose for initial activityconcentrations of between 0.2-4 mCi per mL of cement. Results for doseat other distances would be analogous. For example, in some embodiments,the distance ranges from about 3 mm to about 4 mm. In some embodiments,the distance ranges from about 3.25 mm to about 3.75 mm. In someembodiments, the distance ranges from about 2 mm to about 5 mm. In someembodiments, the distance ranges from less than about 2 mm or greaterthan about 5 mm. For each distance, the central finite difference methodwas used to calculate the percent rate of change in dose per percentrate of change in volume (% Change Dose per % Change Volume) at eachdose-volume data point (squares on FIGS. 11b-11d ). % Change Dose per %Change Volume was then plotted against cement volume, and a logarithmiccurve was fit to the data. FIGS. 11b-11d show the % Change Dose per %Change Volume data for a distance of 3.4375 mm, and the logarithmiccurve fit for all three distances from the cement surface.

As shown in the plots of % Change Dose per % Change Volume versus cementvolume, for all three cement shapes, increasing the implanted volume ofradioactive cement, which increases the total implanted initialactivity, does not yield a proportional increase in the dose at a fixeddistance from the cement surface (3.4375 mm in FIGS. 11b-11d ). (In thecase of the cement cylinder, increasing the volume was due solely toincreasing the cylinder diameter, as the cylinder height remainedconstant.) Thus, unlike a conventional brachytherapy implant, the dosefrom P-32 radioactive bone cement does not necessarily depend on thetotal implanted activity. Furthermore, as the implanted radioactivecement volume increases, the dose at a fixed distance from the cementsurface approaches a constant, maximum value. The low sensitivity ofdose to changes in volume is indicated by % Change Dose per % ChangeVolume and is similar for all of the analyzed shapes and at all threedistances from the cement surface. These shapes are clinically relevantbecause each individual shape or a combination of multiple shapes(cylinders, spheres and/or cubes) can be used to approximate the shapeof actual radioactive cement implants. For example, in some embodiments,cylinders can be combined with cubes, spheres, other cylinders and/orother shapes; cubes can be combined with cylinders, spheres, other cubesand/or other shapes; and spheres can be combined with cylinders, cubes,other spheres and/or other shapes.

These results make it possible to base guidelines for treatment of bonemetastases with radioactive cement solely on the activity concentrationof the cement rather than on the total implanted activity. For example,for a clinically-relevant cement volume of about 2 cm³, % Change Doseper % Change Volume ranges from 0.085-0.155 for all cement shapes anddistances from the cement surface (FIGS. 11b-11d , Table 5). Then, for amaximum allowable % Change Dose of 10% (the maximum deviation from theprescribed dose for a clinical treatment), the corresponding maximumallowable % Change Volume would range from 65-118%. Thus, when theanticipated initial cement volume is 2 cm³, regardless of cement shape,an actual volume of up to 3.3-4.4 cm³ could be implanted withoutchanging the dose by more than 10%. Examples for other initial cementvolumes can be found in Table 5, where the range of % Change Volume foreach initial volume is indicated with bold type.

TABLE 5 % Change Dose per Maximum Allowable Initial % Change Volume at %Change Volume for Cement Volume Various Distances % Change Dose = 10%Shape (cm³) 2.1875 mm 3.4375 mm 4.0625 mm 2.1875 mm 3.4375 mm 4.0625 mmCylinder 0.5 0.19 0.195 0.2 53% 51% 50% Sphere 0.5 0.175 0.19 0.195 57%53% 51% Cube 0.5 0.14 0.14 0.14 71% 71% 71% Cylinder 1 0.155 0.165 0.17565% 61% 57% Sphere 1 0.145 0.165 0.175 69% 61% 57% Cube 1 0.115 0.1150.115 87% 87% 87% Cylinder 2 0.12 0.135 0.145 83% 74% 69% Sphere 2 0.120.14 0.155 83% 71% 65% Cube 2 0.085 0.09 0.09 118%  111%  111%  Cylinder3 0.1 0.115 0.13 100%  87% 77% Sphere 3 0.1 0.125 0.145 100%  80% 69%Cube 3 0.07 0.075 0.075 143%  133%  133%  Cylinder 5 0.075 0.095 0.11133%  105%  91% Sphere 5 0.08 0.105 0.125 125%  95% 80% Cube 5 0.050.055 0.055 200%  182%  182% 

Additional MCNP models were analyzed to demonstrate that the relativeindependence of dose on cement volume (and therefore activity) is due tothe attenuation properties of the cement matrix material, and is notsimply due to the distribution of the radioisotope. These models wereidentical to the models described above, with the exception that theradioactive source was P-32 uniformly distributed within a cylindricalvolume of air instead of bone cement.

Without the shielding effect of the bone cement, a greater proportion ofthe radiation from P-32 escapes the source volume of air and isdeposited within the surrounding bone. Thus, to facilitate comparison ofP-32 in air with P-32 in bone cement, the activity concentration forP-32 in air was scaled so that both P-32 in air and P-32 in bone cementdelivered the same dose (29 Gy) at 3.4375 mm for a clinically relevantsource volume of 2.5 ml. The results are shown in FIGS. 11e and 11f .Unlike the behavior for P-32 in bone cement, the dose at 3.4375 mm forP-32 in air does not approach a maximum value and, in fact, continuouslyincreases with increasing source volume, as shown in FIG. 11e . Theseresults demonstrate that the dose from P-32 in bone cement is relativelyinsensitive to source volume (and therefore total activity) and thatthis characteristic can be attributed to the attenuation properties ofthe bone cement.

Finally, MCNP models were analyzed to demonstrate this characteristicfor P-32 in other matrix materials, as shown in FIGS. 11g and 11h .These models were identical to the cylinder source models describedabove, with P-32 modeled as uniformly distributed within a cylindricalvolume of pure polymethylmethacrylate (PMMA, no barium sulfate added),marrow, solid cortical bone, water, hydroxyapatite, and tantalum. Thedensity of the surrounding bone was 1.22 g/cm³, representing typicalhuman vertebral trabecular bone. Other densities would yield analogousresults.

As before, the activity concentration in each matrix material was scaledso that the same dose (29 Gy) at 3.4375 mm was delivered for a sourcevolume of 2.5 ml. The resulting dose-volume curves and % Change Dose per% Change Volume versus volume curves are very similar for every matrixmaterial (FIGS. 11g and 11h ). These results indicate that the relativeindependence of dose from total activity is a characteristic of P-32uniformly distributed within a wide range of matrix materials, fromlow-density marrow (0.98 g/cm³) to high-density tantalum (16.7 g/cm³).The materials examined here are not all-inclusive and were selected toillustrate that a number of matrix materials, some of which may havebiologically, structurally, or otherwise useful features, could be mixedwith a beta-emitting radioisotope to achieve relative independence ofdose on volume. The resulting mixture may be a cement, a putty-likematerial that is shaped and pressed into place, a liquid or powdercontained in a balloon or bag, etc. Once placed in the body, the dose tothe target would be relatively independent of the volume or shape of thematerial.

To determine the effect of different bone materials on the dosedistribution of radioactive bone cement, eight MCNP models containingthe 15 mm-edge-length cubic volume of radioactive bone cement werecreated, and all bone in the vertebra was modeled as a uniformdistribution of a single bone material. In each model, all of thesurrounding bone was assigned one of the material definitions in Table1.

The dose distribution curves for each model are shown in FIG. 12. As thecortical bone volume fraction of the surrounding bone materialincreases, the dose gradient becomes steeper, indicating that higherdensity bone attenuates the radiation to a greater extent than lowerdensity bone. This may be a clinically important result since thecortical shell separating the vertebral body from the spinal canal wouldthen be expected to enhance the shielding effect of the bone and preventharmful radiation from reaching the spinal cord. This effect may also beimportant in determining dose requirements for targeting a tumorconfined within the vertebral body if regions of very high densitytissue (such as a blastic tumor) exist between the cement source and thetargeted tumor.

Since bone material definitions include both atomic composition anddensity, the effect of bone material was further analyzed byindependently varying atomic composition and density separately.Fourteen additional MCNP models of the 15 mm-edge-length cubic volume ofradioactive bone cement were created, with bone material definitionsbased on material B13 (80.2% marrow/19.8% cortical bone, 1.221 g/cm³density), a bone material that was observed in the trabecular bone ofthe models of the vertebral body. In seven of the MCNP models, thedensity of the surrounding bone material was held constant while theatomic composition was varied among the atomic compositions of seven ofthe other eight material definitions used in Table 1. In the other sevenMCNP models, the atomic composition of the surrounding bone material washeld constant while the density was varied among the densities of theother seven materials.

The dose distribution curves for each of these models are shown in FIG.13 and FIG. 14. When the atomic composition is held constant and thematerial density is varied, the dose distributions resemble those inFIG. 12, in which both the atomic composition and density of the bonematerials were varied (FIG. 13). However, when the density is heldconstant and the atomic composition is varied, the dose distributionsare virtually identical to each other (FIG. 14). Thus, it can beconcluded that the observed differences in dose distributions in FIG. 12are mostly due to the difference in density, rather than atomiccomposition, between the different bone materials. This result may beuseful for evaluation of model accuracy, as it indicates that themodeling method is more sensitive to changes in density than it is tochanges in atomic composition.

Since P-32 can be activated using a number of different methods, some ofwhich may produce additional radioisotopes, it is necessary to determinethe effect of the actual composition of the radioactive compound on dosedistribution. The MCNP models described to this point have assumed apure P-32 radioactive source, which would be the case for a compoundthat is synthesized with P-32. However, a P-32 source that is also underconsideration is manufactured in a way that produces trace amounts ofcalcium-47 (Ca-47, 4.5 day half-life) and its daughter scandium-47(Sc-47, 3.4 day half-life). To determine the effect of the presence ofadditional radioisotopes on the predicted dose distribution, twoadditional MCNP models were created and analyzed, in which the 15mm-edge-length cubic volume of radioactive bone cement modeled abovecontained Ca-47 and Sc-47 source definitions. The resulting dosedistributions were added to the P-32 dose distributions, taking intoaccount the half-life of each radioisotope and its relative initialactivity (0.6 μCi of each radioisotope per 1 mCi of P-32).

There was no visible difference in the dose distributions for the pureP-32 radioactive source and the P-32/Ca-47/Sc-47 radioactive source(FIG. 15). Although both Ca-47 and Sc-47 decay with a small amount ofgamma emissions, their initial activities relative to P-32 are extremelysmall and their half-lives are relatively short, resulting in anegligible effect on the dose distribution of the entire compound.Although this effect can be confirmed for additional radioactivecompounds, it is likely that other methods of synthesizing P-32 as theprimary radioisotope would yield similarly insignificant quantities ofcompound impurities.

To determine the effect on dose distribution of the specific type ofbone cement used, four additional MCNP models of the 15 mm-edge-lengthcubic volume of radioactive bone cement modeled above were created andanalyzed. In these models, the original P-32 radioisotope source wasuniformly distributed within several types of bone cement commonly usedin orthopaedic procedures. Three models examined bone cements used inthe vertebroplasty and kyphoplasty procedures that radioactive bonecement would be used with to treat spinal metastases: ArthroCareParallax® Bone Cement, ArthroCare Parallax® Bone Cement with TRACERS®Bone Cement Opacifier, and Stryker Spineplex® Bone Cement. Additionally,one model examined Stryker Surgical Simplex® P Bone Cement, which mightbe used in a percutaneous hip repair procedure. Although these brandsare very similar polymethylmethacrylate bone cements, their exactcompositions vary.

The dose distributions curves for each model are virtually identical(FIG. 16), indicating that variations in the composition of each of theanalyzed bone cements do not have a significant effect on the resultingdose distributions. Given the similarity in atomic composition for eachof these bone cement formulations, this result is to be expected.Although it would be necessary to confirm this effect for additionalbone cements, most PMMA bone cement formulations are very similar andlikely would not significantly affect the resulting dose distribution,meaning that the clinical feasibility of radioactive bone cement islikely independent of the specific type of PMMA used.

In some embodiments, the method for treating a target tissue includesidentifying a vertebral tumor; determining its distance from the cementthat would be injected during vertebroplasty; and, based on adose-to-depth parameter, determining the activity concentration todeliver a target dose at a specified distance from the surface of thecement.

Accordingly, as the vertebral tumor is within the specified distancefrom the surface of the cement, additional activity contained withincement delivered elsewhere within the vertebral body will not affect thedose distribution in the target tissue.

Dose distributions predicted using the radiation transport modelingmethod developed were compared to those measured experimentally withradiochromic film. As necessary, experimental sources of error wereidentified and the Monte Carlo models were modified until the predictedand measured dose distributions agreed within the experimentaluncertainty.

Nine human cadaveric vertebrae were obtained from three female donors(Table 5). In each vertebra, a flat-bottom cylindrical hole was createdin the vertebral body, entering through the superior face and to a depthof about 75% of the vertebral body height, using a 6.35 mm diameter (forthe C7 and T1 vertebrae) or a 9.53 mm diameter (for the T5, T6, T11 andT12 vertebrae) drill bit and end mill bit. This hole would allow for theplacement of a preformed cylinder of radioactive bone cement within thevertebral body during the subsequent laboratory experiment. Thedimensions of each cylindrical hole were measured and recorded, and analuminum mold was fabricated for molding appropriately sized cylindersof radioactive bone cement. A precision band saw with a diamond-coatedblade (EXAKT 300CP, EXAKT Technologies, Inc., Oklahoma City, Okla., USA)was then used to create 0.25 mm thick slots within the vertebral bodyfor placement of radiochromic film. These slots were approximatelyparallel to the axis of the cylindrical hole and oriented in the coronaland sagittal planes of the vertebrae. At their closest point, the slotswere about 0.1 mm to 7 mm from the surface of the cylindrical hole, asmeasured on the superior face of the vertebral body. Coronal slots wereposterior to the cylindrical hole, intended to measure the doseapproaching the spinal canal. Sagittal slots were lateral to thecylindrical hole, in either or both directions (FIG. 17; arrow indicatescylindrical hole for placement of radioactive cement cylinder).

TABLE 5 Donor Age (years) Cause of death Vertebral specimens (study ID)1 69 Anoxic encephalopathy T1 (0101), T6 (0106), T12 (0112) 2 80 Cardiacarrest T1 (0201), T5 (0205), T12 (0212) 3 84 Artherosclerotic vasculardisease C7 (0300), T4 (0304), T11 (0311)

A silicone mold was created around the posterior element of eachvertebra to hold the specimens in place. CT scans were obtained with thevertebrae immersed in water to minimize streak artifacts (GE DiscoveryVCT PET/CT, standard reconstruction, 80 kVp, 280 mAs). To enableaccurate measurement of apparent wet bone mineral density (BMD), thevertebrae from donor 1 were scanned with 0.625 mm pixels and thevertebrae from donors 2 and 3 were scanned with 0.3125 mm pixels. Thevertebrae from donors 2 and 3 were scanned with smaller pixels in aneffort to refine model resolution. However, this did not have thedesired effect, and the CT data were later reconstructed to provide0.625 mm pixels. A plastic calibration phantom containing chambers thatwere radiographically equivalent to 0, 75, and 150 mg cm⁻³ of calciumhydroxyapatite in water (Image Analysis Inc., Columbia, Ky.) wasincluded in each scan. To minimize the size of the subsequent MonteCarlo model while maintaining adequate resolution, CT scans wereobtained with contiguous 1.25 mm thick slices.

In-house software was developed and used to transform the CT scan datafor each vertebra into a Monte Carlo N-Particle (MCNP) model (X-5 MonteCarlo Team 2005) consisting of a three-dimensional rectangular latticeof 0.625 mm×0.625 mm×1.25 mm voxels (FIG. 18). Bone in the model wasrepresented by as many as thirty bone material definitions, with bothtrabecular and cortical bone represented by a spectrum of complementaryvolume fractions of bone marrow and solid cortical bone, ranging from100% bone marrow to 100% solid cortical bone. Each voxel of bone wasassigned a bone material (i.e. one of the thirty bone volume fractions)by converting its quantitative CT density (ρ_(QCT), g cm⁻³) to ashdensity (ρ_(ash), g cm⁻³)(ρ_(ash)=0.0633+0.887 ρ_(QCT), r=0.997), andthen converting ρ_(ash) toapparent wet BMD (ρ_(wet), g cm⁻³)(ρ_(wet)=1.79ρ_(ash)+0.0119, r=0.992). Then, using the ruleof mixtures,the real density of the bone tissue plus marrow was calculated by addingthe density of the complementary volume fraction of marrow to apparentwet BMD. The atomic composition of each bone material was alsocalculated using the rule of mixtures, where the atomic compositions ofthe bone (H: 3.4%, C: 15.5%, N: 4.2%, O: 43.5%, Na: 0.1%, Mg: 0.2%, P:10.3%, S: 0.1%, Ca: 22.5%) and marrow (H: 11.5%, C: 64.4%, N: 0.7%, O:23.1%, Na: 0.1%, S: 0.1%, Ca: 0.1%) volume fractions were given by priorstudies. Since the vertebrae were not immersed in water during thesubsequent laboratory experiment, all voxels that were outside the bonewere assigned the density and atomic composition of air. The cylindricalhole that was previously created within each vertebral body wasidentified on the CT scans and the constituent voxels within that holewere assigned the properties of Parallax® PMMA bone cement (ArthroCareCorp., Sunnyvale, Calif., USA) (FIG. 18). FIG. 18 shows a transversecross-section of a modeled vertebra. The cylindrical drill hole isapparent in (a) the CT scan image and was modeled as a volume ofradioactive bone cement (white circle) in (b) the MCNP model. Aphosphorus-32 (P-32) radionuclide source was modeled as uniformlydistributed within all bone cement voxels, with a complete energyspectrum from medical internal radiation dose (MIRD) data. P-32 is anideal radionuclide for radioactive bone cement due to its high-energybeta emissions (maximum: 1.71 MeV), clinically relevant half-life (14.3days), and prior use as a radiopharmaceutical for pain palliation inpatients with bone metastases.

Each voxel in the model included a pulse-height energy distributiontally, and thirty million particle histories were simulated with MonteCarlo N-Particle eXtended v. 2.5.0 (MCNPX, Los Alamos NationalLaboratory, Los Alamos, N. Mex., USA, 2005) using the defaultcross-sections. The presence of the cement within the model ensured thatall self-shielding effects were accurately represented. For each voxeltally, the energy deposited per source particle was used to calculatethe dose rate per unit of initial activity, hereafter referred to simplyas ‘dose rate’, with units of Gy/h/mCi. Matlab R2006a (The Mathworks,Inc., Natick, Mass., USA) was first used to visually confirm that thedose distributions were axisymmetric by generating isodose contour linesfor three dose rates within the vertebral body: 0.3 Gy/h/mCi, 0.5Gy/h/mCi and 2 Gy/h/mCi. Once confirmed to be axisymmetric, the dosedistribution for each specimen was characterized by a single radialdepth-dose curve, i.e. an exponential curve of dose rate versus radialdistance from the surface of the radioactive cement. To minimize localeffects, the radial depth-dose curve was averaged over four radialdirections (anterior, posterior, left lateral, right lateral) withineach of three consecutive transverse planes near the center of thecylinder of cement. Tally results were assumed to be at the center ofeach voxel. To ensure adequate precision of the model data, thepredicted radial depth-dose curves were calculated using only thosetallies with a relative error (X-5 Monte Carlo Team 2005) less than0.05.

The dose distribution in each vertebra was measured experimentally usingradiochromic film, a radiation dosimetry tool that consists of a thinactive layer of monomeric molecules sandwiched between two thinpolyester sheets. The monomeric molecules polymerize upon exposure toionizing radiation, resulting in a color change to blue that isdependent on the absorbed dose of the film. In this study, GafchromicEBT radiochromic film (Lot #47277-061, Exp. Date October 2009,International Specialty Products, Wayne, N.J., USA) was selected for itsease of use, high spatial resolution, and electron energy- anddose-rate-independent response. Dose calibration was performed byirradiating 27 pieces of the film at doses of 0-15 Gy using a 12 MeVelectron beam produced by a Clinac 21-EX linear accelerator (VarianMedical Systems, Inc., Palo Alto, Calif., USA), calibrated according tothe TG-51 protocol. The 12 MeV electron beam was selected because it hasa broad depth of dose maximum, which minimizes the effect of positioninguncertainties in the calibration setup. Each piece of film was placed atthe depth of dose maximum (dmax=28 mm) in a solid water phantom andirradiated under calibration conditions of 100 cm source-to-surfacedistance and 15×15 cm² size electron applicator. Each piece of film wasthen scanned on an Epson VX700 flatbed scanner (Epson America, Inc.,Long Beach, Calif., USA) at 122 dpi with the film in landscapeorientation (with respect to the original, uncut sheets) relative to theaxis of the scanner bed. Red channel pixel intensity was converted tooptical density, and the average optical density within a 100 pixel×200pixel region in the center of each film was calculated. The net opticaldensity (netOD) for each film was calculated relative to the opticaldensity of the unexposed film, and plotted against the correspondingdose level for that film. A calibration equation was described using athird-order polynomial function and used to determine the radiochromicfilm dose rates in the experiment.

For the experiment, P-32 was mixed with Parallax® bone cement powder andshaken to ensure a uniform distribution of the radionuclide within thecement powder. The liquid monomer was added and the cement was mixedaccording to the manufacturer's recommended procedure, creatingradioactive bone cement. The cement was prepared under the approval andguidance of the Environmental Health and Safety office at the Universityof California, Irvine, with all steps taken to minimize the risk ofharmful radiation exposure. The radioactive cement was then injectedinto the aluminum molds that were fabricated previously for makingcement cylinders, after which the cured radioactive cement cylinderswere inserted into the cylindrical hole of the appropriate vertebralbody. The total initial activity contained within each cylinder andimplanted into each specimen was calculated from the manufacturer'sassayed level of activity, after accounting for decay from the assaydate to the date of the experiment, and ranged from 0.062 mCi (2.294MBq) to 0.36 mCi (13.32 MBq), depending on the size of each implantedcylinder.

After the creation of the cylindrical specimens, the excess radioactivecement was injected into a plastic tube (6 cm length, 5 mm innerdiameter, 0.7 mm wall thickness), allowed to cure, and placed directlyon top of a piece of radiochromic film for 24 hours. The exposedradiochromic film was then scanned using the procedures describedpreviously. The uniformity of the dose distribution and, therefore, theuniformity of the P-32 distribution within the cement, was thenevaluated by calculating the standard deviation as a percentage of themean of the dose rate along a straight line on the axis of the tube.

Pieces of radiochromic film that had been cut to size and labeled wereplaced within the coronal and sagittal slots that had been previouslycut in the vertebral body (FIG. 19). The exposure time for each piece offilm was in the range of 6-168 h, selected to maximize contrast whilepreventing overexposure, given the expected dose rate at each filmlocation. When one piece of film was removed from the vertebral body, areplacement scrap piece was inserted in its place to maintain theattenuation characteristic across the plane of the film. At theconclusion of the experiment, the exposed film pieces were scanned asdescribed previously and the experimental dose (dose over theexperimental exposure period) measured by each piece of film wasquantified using the calibration equation obtained previously.

The maximum experimental dose measured in any pixel on each piece offilm was determined and divided by the corresponding exposure time andinitial activity to calculate the maximum experimental dose rate(Gy/h/mCi) for each piece of film. Analogous to the MCNP-predicted dosedistribution, the measured dose distribution for each specimen wasassumed to be axisymmetric about the radioactive cement implant and wascharacterized by a radial depth-dose curve. For each vertebra consideredseparately, the measured radial depth-dose curve was generated byplotting the maximum dose rate for each piece of film within thatvertebra versus the shortest radial distance from the surface of theradioactive cement to the corresponding film.

Accuracy of the MCNP models was evaluated by comparing the predicted andmeasured dose distributions. For radial distances of 1 mm, 2 mm, and 3mm on the predicted depth-dose curve, the absolute value of thehorizontal distance between the predicted and measured curves wascalculated for each specimen and averaged across all specimens. Thisapproach is recommended by the International Commission on RadiationUnits and Measurements (1987) for high-gradient regions of depth-dosecurves. In the low-gradient region of the depth-dose curves, thevertical difference (measured dose rate minus predicted dose rate)between the depth-dose curves at radial distances of 5 mm and 6 mm wascalculated for each specimen and averaged across all specimens.

As a more rigorous evaluation of model accuracy, the predicted andmeasured dose distributions were evaluated for agreement within theexperimental uncertainty. Since dose rate decreased exponentially withdistance, regression analysis (SigmaStat, San Jose, Calif., USA) wasused to compute log-linear depth-dose curves, i.e. linear relationshipsbetween ln(dose rate) and radial distance, for the predicted andmeasured data for each specimen. Additionally, the 95% confidenceinterval (CI) of the measured log-linear depth-dose curve wasdetermined. The models were deemed to be accurate when the dosedistributions agreed within the experimental uncertainty, i.e. when thepredicted log-linear depth-dose curve fell within the 95% CI of themeasured log-linear depth-dose curve.

A potential source of uncertainty is related to a loss of marrow fromwithin the vertebral body during specimen preparation. The modeled bonematerials were based on the CT densities of bone that contained marrowor water within the trabecular pores, since marrow may have beendisplaced from the vertebral body when the vertebrae were immersed inwater for CT scanning. However, since the vertebrae were removed fromthe water after CT scanning, the marrow that had been displaced by watermay have been replaced by air during the experiment, potentially causingthe experimental condition to be modeled somewhat inaccurately. Todetermine whether model inaccuracy could be attributed to this source ofuncertainty, models that were not accurate according to the abovedefinition were modified by reducing the density of the bone marrowconstituent of the bone material definitions until the predicted andmeasured dose distributions agreed within the experimental uncertainty.This reduction in bone marrow density was intended to represent areduced quantity of marrow within each specimen.

Specimen 0201 (Table 5, row 2, column 4) was destroyed during experimenthandling, leaving eight specimens for evaluation. The isodose contourplot of the predicted dose distribution within each vertebral bodyconfirmed an axisymmetric distribution about the cylindrical radioactivecement source and rapidly decreasing dose with increasing radialdistance from the cement surface, as shown in FIG. 20. Isodose linesrepresent constant dose rates of 0.3 Gy/h/mCi, 0.5 Gy/h/mCi, and 1.9Gy/h/mCi, from the largest to the smallest circles.

In the high-gradient region of the depth-dose curves, the averageabsolute value of the horizontal distance from the predicted curve tothe measured curve was 0.27, 0.49 and 0.90 mm at radial distances of 1,2, and 3 mm, respectively, from the surface of the radioactive cementsource. In the low-gradient region of the depth-dose curves, the averagevertical difference from the predicted depth-dose curve to the measureddepth-dose curve was 0.055 and 0.033 Gy/h/mCi at 5 and 6 mm,respectively (FIG. 21). FIG. 21(a) illustrates predicted (squares, solidline) and measured (circles, dashed line) radial depth-dose curves forspecimen 0101, and FIG. 21(b) predicted (squares, solid line) andmeasured (circles, dashed line) radial depth-dose curves for specimen0212.

FIG. 22 illustrates predicted (squares, solid line) and measured(circles, dashed line) log-linear depth-dose curves for specimens (a)0101 and (b) 0212. For four of the eight specimens, the predicted andmeasured dose distributions agreed within the experimental uncertaintyover the entire radial distance range (FIG. 22(a)). For the remainingfour specimens, the predicted log-linear depth-dose curve fell withinthe 95% CI of the measured log-linear depth-dose curve for distances upto ˜2 mm, but consistently understated the measured dose rate at pointsfar from the cement surface (i.e., at distances greater than ˜2 mm)(FIG. 22(b)). The bone marrow density in these models was decreased by20-40% to account for an absence of marrow that was observed in thetrabecular pores of some specimens, as illustrated by a post-experimentphotograph (FIG. 23) showing open trabecular pores resulting from marrowloss during the experimental specimen preparation procedure. Thisresulted in predicted and measured dose distributions that agreed withinthe experimental uncertainty, as illustrated by FIG. 24 which showspredicted (squares, solid line) and measured (circles, dashed line)log-linear depth-dose curves for the modified MCNP models for specimens(a) 0212 (40% marrow reduction) and (b) 0311 (20% marrow reduction). Forall four modified MCNP models, decreasing the bone marrow density by20-40% resulted in dose distributions that agreed within theexperimental uncertainty.

The above-described radiation transport modeling method canautomatically generate anatomically correct, patient-specific, CTscan-based MCNP models of vertebrae containing radioactive bone cement.The accuracy of the modeling method was evaluated by comparing dosedistributions calculated by the models to those measured in humancadaveric vertebral bodies in which radioactive bone cement had beenimplanted. The results presented indicate that these models can predictmeasured dose distributions with clinically relevant accuracy and withinthe experimental uncertainty, making this modeling method a usefulanalytical tool for developing radioactive bone cement to treat spinalmetastases.

The radiochromic film used to evaluate the uniformity of thedistribution of P-32 within the radioactive cement revealed that thestandard deviation of the dose rate along the axis of the cement-filledtube was 0.33% of the mean. This result indicates that the P-32 wassufficiently mixed within the radioactive cement, thereby validating theuniform distribution of radionuclide within the MCNP cement voxels.

In the high-gradient region of the depth-dose curves, the averagehorizontal distances between the predicted and measured radialdepth-dose curves can be compared to the results of a first study, thatmeasured differences of 0.2-0.5 mm, and a second study, that measureddifferences of 0.5-0.7 mm (in both of these studies, it was not statedwhether these are absolute or signed values). Our average absolutedifferences of 0.27-0.90 mm are approximately the same as those ofprevious studies, a notable result considering the heterogeneity andinherent complexity of cadaveric vertebral bodies compared to thehomogeneous solid water and “tissue-substitute” plastic phantoms usedpreviously. Our results indicate that if the MCNP models were used topredict the dose rate within the vertebral body at a radial distance of,e.g., 2 mm from the surface of the radioactive cement, the actual radialdistance at which that dose rate would occur might differ by about 0.2mm. This difference is much lower than the 2-4 mm criteria ofacceptability established as the benchmarks for EBRT treatment planningaccuracy.

In the low-gradient region of the depth-dose curves, the averagevertical differences between the predicted and measured radialdepth-dose curves indicate that if the MCNP models were used to predictthe dose rate within the vertebral body at a radial distance of, e.g., 6mm from the surface of the radioactive cement, the actual dose rate atthat distance might be about 0.033 Gy/h/mCi greater than the modelprediction. For the levels of activity that were implanted in thisstudy, this difference corresponds to a predicted lifetime dose of0.28-1.6 Gy when the actual lifetime dose would be 1.3-7.5 Gy. Dependingon the location of the radioactive bone cement within the vertebralbody, this region of the depth-dose curve may be used for dosimetry ofthe spinal cord. In that case, this dose underestimation might beimportant, depending on the patient's history of spinal cord irradiation(e.g., prior EBRT) and the volume of cord affected, among other factors.This type of information will guide the development of clinicaltreatment planning for using radioactive bone cement to treat spinalmetastases.

It is noteworthy that only tallies with a relative error less than 0.05were analyzed, and the MCNP-predicted radial depth-dose curves wereextrapolated to radial distances beyond the range of the tally resultsto which they were fit. Although this extrapolation may have limited theaccuracy of the predicted dose rates in the low-gradient region of thedepth-dose curves, this approach was necessary to ensure that thedepth-dose curves were based on tallies that had an optimal relativeerror. A number of variance reduction techniques in MCNP may be used toextend the radial distance at which optimal tally results can beobtained. However, that was beyond the scope of this study.

For the more rigorous evaluation of model accuracy, the 95% CI of themeasured loglinear depth-dose curve reflected the uncertainty associatedwith dose measurements using radiochromic film, which can be high as±15%, as well as uncertainty in the radial distance measurements used tocompute the depth-dose curve. Models for four of the specimens predictedthe measured dose distribution within this uncertainty withoutmodification. For the remaining four specimens, reducing the marrowdensity showed that the understatement of dose rate by the unmodifiedmodels could be attributed to a loss of bone marrow from the vertebralbody. The volume of marrow lost from each specimen could not bequantified, and marrow loss was neither uniform within each specimen norconsistent across all specimens. However, visual observation indicatedthat marrow loss generally seemed to be most extensive in the specimensthat required model modification. Thus, although the magnitudes of themarrow density reductions are somewhat arbitrary, the agreement betweenthe predicted and measured dose distributions after adjusting for marrowloss, and the agreement of the other four models even withoutmodification, demonstrates that the modeling method is fundamentallysound. Hence, in intact vertebrae or in experiments that minimize marrowloss, we can expect that this modeling method can be used to predictdose distributions in vertebrae containing radioactive bone cement.

This study employed P-32 as the radionuclide for radioactive bonecement. A number of other radionuclides might be used (and potentiallyin combination), such as strontium-89 (Sr-89), yttrium-90 (Y-90) andrhenium-188 (Re-188). However, alternative radionuclides andcombinations thereof may produce very different dose distributions thanthose evaluated in this study, since the energy spectrum and particleemission type may be much different from P-32. The accuracy of MCNPmodels for radionuclides other than P-32 can be evaluated in a mannersimilar to this study.

The MCNP modeling method was evaluated using cylindrical radioactivebone cement specimens. However, clinical vertebroplasty may involvecement distributions that are more complex and involve cement-boneinterdigitation. The cylindrical cement specimens enabled a repeatable,practical experiment in which the geometry of the radioactive sourcecould be accurately modeled from CT scan images. This experiment allowedthe MCNP models to be reliably evaluated with respect to radiationtransport through mixtures of bone and marrow, as well as through theradioactive cement itself. The agreement between the predicted andmeasured dose distributions indicates that the fundamental principlesunderlying the CT scan-based modeling method are sound, and moresophisticated models involving clinically relevant cement distributionscan be developed and analyzed.

With its fundamental principles now established, the CT scan-based MCNPmodeling method presented in this study can be used as an analyticaltool for use in the development of using radioactive bone cement totreat spinal metastases. Use of the modeling method will enable asystematic analysis of many issues, including the distance from thecement at which a therapeutic dose can be delivered to the bone; theextent to which the implanted activity, bone density, and presence oflesions change this distance; and the resulting maximum volume ofbone/tumor that can be treated. The models will also enable estimates ofthe absorbed dose in the adjacent bone and the cement itself, factorsthat might potentially lead to degradation of material properties. Theseissues, among many others, will determine the feasibility of usingradioactive bone cement to treat spinal metastases and will help todefine guidelines for its clinical use.

A radiation transport modeling method was presented to calculate dosedistributions within vertebrae containing radioactive bone cement. Thisstudy marked the first-ever attempt to measure such dose distributions,and the accuracy of the modeling method was evaluated by comparingmodel-predicted dose distributions to those measured experimentally.Differences between the high-gradient regions of the predicted andmeasured radial depth-dose curves were comparable to differencesevaluated using homogenous plastic phantoms and are likely to beclinically insignificant. Differences in the low-gradient regions of thedepth-dose curves may be important in situations involving prior spinalirradiation, and this information will guide the development of clinicaltreatment planning for using radioactive bone cement to treat spinalmetastases. Using a more rigorous evaluation of model accuracy, modelsfor four of the specimens predicted the measured dose distributionwithin the experimental uncertainty without modification. For theremaining four specimens, reducing the marrow density showed that whenmarrow loss is accounted for, this modeling method can accuratelypredict dose distributions in vertebrae containing radioactive bonecement. This modeling method is a valuable tool for development ofradioactive bone cement as an alternative to the conventional two-stepapproach to treating spinal metastases.

The following algorithm may be used for treatment planning, whichincludes determining the distance from the surface of the cement totissues that will be spared (e.g., neurologic tissues), the prescribedactivity concentration, the approximate location(s) at which the cementmay be injected, and the planned dose distribution in the target tissuesand structures to be spared. The physician first identifies the lesionsand tissues to be spared on images from MRI, CT or other imagingmodalities that provide accurate measurement of distances to the keyanatomical structures. The physician then specifies maximum tolerabledose to each tissue to be spared. For example, 45 Gy to the spinal cord.

From FIG. 25 or an equivalent table or website that will be available tothe physician, and assuming the maximum tolerable dose to the tissues,the physician determines the minimum distance from the cement surface toeach tissue for each activity concentration. A “conservative” approachmay be used to ensure safety. Thus, in cases with lytic lesions, thecurves for pure marrow may be used to determine this distance. Forexample, for 1 mCi/ml, a distance of at least 4 mm would provide lessthan 45 Gy to the spinal cord, regardless of bone density. For 4 mCi/ml,a distance of about 5 mm between the cement surface and the spinal cordwould be acceptable. Because each distance will be associated with anuncertainty due to the uncertainty in the computed distance (based onthe dosimetry model validation experiments), a margin of safety may bebuilt into the tools to be used by the physician. If there is asubstantial shell of cortical bone between the cement and the tissue tobe spared, the physician may wish to account for the protective effectof the cortex, which will reduce the dose to the tissue to be spared.Such a factor may be included in the tools for the physician, which willallow a greater dose to be delivered to the target. Additional dosimetrycurves for bone with blastic lesions will allow the physician todetermine the effect of blastic lesions on the dose to the tissues to bespared. These curves will also tell the physician the extent to whichthe particular activity concentration will allow the radiation topenetrate through the dense bone.

FIG. 25 depicts log-linear depth-dose curves for the vertebral body witha 15-mm cubic volume of radioactive bone cement which indicate that thedose rapidly decreases with distance from the surface of the cement.Depth-dose curves are shown for the actual vertebral bone density (solidlines) and for zero bone density (100% marrow) (dotted lines), forinitial activity concentrations of 1 mCi/ml (thick lines) and 4 mCi/ml(thin lines). Other activity concentrations that may be available (2 and3 mCi/ml) are not shown for clarity. For activity concentrations of 1mCi/ml to 4 mCi/ml, the distance at which a lifetime dose of at least 10Gy is delivered increases by less than 0.6 mm when the bone densitychanges from the actual density to that of pure marrow.

FIG. 26 illustrates a schematic of dosimetry procedure to be performedusing transverse images through the vertebral body. Only one nerve rootis shown for clarity.

Once the physician determines the distance between the tissue to bespared and the cement surface for each tissue to be spared (e.g., eachnerve root and the spinal cord), the physician marks this distance foreach activity concentration on at least one transverse image through thevertebra (as shown in FIG. 26 by the dotted lines). If only one image isused, it may be the one that results in the most conservative treatmentplan, which would be the image in which the sensitive structure(s) areclosest to the target.

The result of the previous step will then determine the activityconcentration(s) that can safely be used. If the tumor lies beyond allmarked distances for an activity concentration of 4 mCi/ml (e.g., in thespeckled area in FIG. 26), then an activity concentration of 4 mCi/mlcan be prescribed, and the cement can be safely injected to within theline labeled “ . . . for 4 mCi/ml.” If the tumor lies completely in thearea between the 1 mCi/ml and 4 mCi/ml lines (hatched area in FIG. 26),the lower activity should be used, and cement can be safely injected towithin the 1 mCi/ml line. If a tumor or portion of a tumor falls withinthe marked distance for the lowest activity concentration, the cementmay only be injected up to that marked distance. The tumor will stillreceive a substantial radiation dose, but that dose will decrease withdistance as shown in FIG. 25, and the tissues to be spared will not beharmed.

What is claimed:
 1. A radioactive material for treating a target tissuein a patient's body, comprising: a matrix material for placement withinthe patient's body; and a beta-emitting radioisotope mixed with thematrix material forming a radioactive material wherein, when placed adistance from the target tissue, the radioactive material delivers adose to the target tissue that is independent of a total volume of theradioactive material placed in the patient's body, wherein aconcentration of the beta-emitting radioisotope is between about 0.1 andabout 4 mCi per ml of the matrix material.
 2. A radioactive material fortreating a target tissue in a patient's body, comprising: a matrixmaterial for placement within the patient's body; and a beta-emittingradioisotope mixed with the matrix material forming a radioactivematerial wherein, when placed a distance from the target tissue, theradioactive material delivers a dose to the target tissue that isindependent of a total volume of the radioactive material placed in thepatient's body, wherein, when the radioactive material is placed in thepatient's body, only emissions from the radioisotope within about 2.5 mmof a surface of the radioactive material that is closest to the targettissue reach the target tissue.
 3. A radioactive material for treating atarget tissue in a patient's body, comprising: a matrix material forplacement within the patient's body; and a beta-emitting radioisotopemixed with the matrix material forming a radioactive material wherein,when placed a distance from the target tissue, the radioactive materialdelivers a dose to the target tissue that is independent of a totalvolume of the radioactive material placed in the patient's body,wherein, when the radioactive material is placed in the patient's body,only emissions from the radioisotope within about 1.9 mm of a surface ofthe radioactive material that is closest to the target tissue reach thetarget tissue.